OPINION
COLE, Circuit Judge.Plaintiff-Appellant Robert Lee Barnett is a Tennessee prisoner who appeals the dismissal, under 28 U.S.C. §§ 1915(e)(2)(B)(ii) and 1915A, of his pro se complaint. His complaint, filed under 42 U.S.C. § 1983, alleged that Defendants-Appellees Shelby County and its employees and officials denied him adequate medical care and mishandled his grievances. The district court dismissed Barnett’s complaint for failure to state a claim, but we find that some of his claims are adequate to survive dismissal: namely, the failure-to-treat claims against defendants Terrie and Cooper. For that reason, we AFFIRM in part and REVERSE in part the district court’s dismissal, and REMAND for further proceedings consistent with this opinion.
I.
We take all facts “from the [cjomplaint, since those were the facts available to the district court.” Williams v. Curtin, 631 F.3d 380, 382 (6th Cir.2011). In 2002, Barnett was incarcerated in Shelby County and allegedly received improper treatment and counseling for tuberculosis. In June 2004, also while incarcerated in Shelby County, Barnett claims he sought treatment for tuberculosis yet again, but received only delayed treatment.
On June 26, 2004, Barnett was to receive ibuprofen from Nurse Terrie, but she incorrectly gave him Dilantin, the seizure medication of another patient. Shift Officer J. Hicks sent him to the medical unit without an escort after determining that Barnett took the wrong medicine. On the way to the medical unit, Barnett grew dizzy and fell down the escalator, sustaining a head injury and headaches as a result. No one administered any treatment to Barnett after this injury.
On September 16, 2004, Barnett filed his pro se complaint in the United States District Court for the Western District of Tennessee. The district court dismissed his complaint for failure to exhaust on February 17, 2006, but we reversed that dismissal and reinstated Barnett’s complaint on June 7, 2006, Barnett v. Luttrell, No. 06-5438 (6th Cir. June 7, 2007). On remand, the district court again dismissed Barnett’s complaint, this time largely for failure to state a claim. Barnett timely appealed.
II.
We review de novo the district court’s dismissal under §§ 1915(e)(2) and 1915A. Grinter v. Knight, 532 F.3d 567, 571-72 (6th Cir.2008). To avoid dismissal, “a complaint must contain sufficient factual matter, accepted as true, to ‘state a claim to relief that is plausible on its face.’ ” Ashcroft v. Iqbal, - U.S. -, 129 S.Ct. 1937, 1949, 173 L.Ed.2d 868 (2009) (emphasis added) (quoting Bell Atl. Corp. v. Twombly, 550 U.S. 544, 570, 127 S.Ct. 1955, 167 L.Ed.2d 929 (2007)). However, “we are mindful to construe [a pro se litigant’s] arguments liberally.” El Bey v. Roop, 530 F.3d 407, 413 (6th Cir.2008).
Barnett appeals the denial of only a subset of his claims: those pertaining to M. Love, Nurse Terrie, Shift Officer J. Hicks, Medical Administrator Tony Coo*787per, Nurse Webb, Dr. Stipanuk, Shelby County Sheriff Mark H. Luttrell, Shelby County, and Correctional Medical Services (“CMS”). His complaints regarding these parties fall into seven general categories: (1) failure to diagnose correctly his tuberculosis in 2002; (2) failure to remedy or act on his tuberculosis in 2004; (3) administration of Dilantin instead of ibuprofen; (4) failure to accompany him to the medical unit after administration of Dilantin, resulting in his fall down the escalator; (5) failure to treat his headaches and other pain resulting from that fall; (6) failure to adequately train and supervise prison personnel; and (7) general inappropriate handling of his grievances.
As an initial matter, we reject two of the arguments Barnett makes for procedural and jurisdictional reasons. Barnett’s arguments relating to events in 2002 are time-barred, see Tenn.Code Ann. § 28-3-104(a)(3) (one-year statute of limitations for section 1983 claims in Tennessee); Hughes v. Vanderbilt Univ., 215 F.3d 543, 547 (6th Cir.2000) (acknowledging the same), and Barnett gives us no reason to exempt his claims here. Also, Barnett’s tuberculosis claims include the argument that defendants improperly released him. into the general prison population, seemingly because of the risk he posed to other inmates. Barnett, however, does not have standing to raise arguments on behalf of others. See Jones v. Caruso, 569 F.3d 258, 276-77 (6th Cir.2009). We therefore affirm the district court’s dismissal of both of these claims.
Turning to the merits, we note that Barnett’s claims allege infringement of two different constitutional rights: First Amendment access to the courts and Eighth Amendment denial of medical treatment.
A. First-Amendment Claim
Barnett alleges that Love did not properly deal with Barnett’s grievances, and that Love falsified various of Barnett’s information in relation to the grievances. In effect, Barnett appears to argue that Love did not follow the grievance procedure and acted in a manner that frustrated Barnett’s attempts to gain relief through that procedure.
Prison officials are not liable under § 1983 for denying or failing to act on grievances. Grinter v. Knight, 532 F.3d 567, 576 (6th Cir.2008). They are liable, however, for frustrating a prisoner’s First Amendment right to access the courts. Kensu v. Haigh, 87 F.3d 172, 175 (6th Cir.1996). To state a violation of this right, a prisoner must allege that a prison official’s conduct caused him an actual injury, such as frustration of a particular legal claim. Hadix v. Johnson, 182 F.3d 400, 405-06 (6th Cir.1999). Barnett identifies no injury from this alleged frustration, so his First Amendment claim must fail. Because this violation is the only basis for recovery from Love that Barnett has pursued on appeal, the district court properly dismissed Love from this litigation.
B. Eighth-Amendment Claims
The Eighth Amendment prohibits prison officials from “unnecessarily and wantonly inflicting pain” on prisoners by acting with “deliberate indifference” to their “serious medical needs.” Blackmore v. Kalamazoo Cnty., 390 F.3d 890, 895 (6th Cir.2004) (internal quotation marks and citation omitted). Such a claim has both a subjective and objective component. Id. The objective component mandates a sufficiently serious medical need. Id. The subjective component regards prison officials’ state of mind. Id. Deliberate indifference “entails something more than mere negligence, but can be satisfied by something *788less than acts or omissions for the very purpose of causing harm or with knowledge that harm will result.” Id. at 895-96 (internal quotation marks and citations omitted). The prison official must “be aware of facts from which the inference could be drawn that a substantial risk of serious harm exists, and he must also draw the inference.” Id. at 896 (internal quotation marks and citation omitted).
1. Defendant Terrie
Barnett alleges that Terrie, a nurse, gave him Dilantin, an anti-seizure medication, rather than the ibuprofen he was supposed to receive. He alleges further that she “left the ‘scene’ of the incident without supervision of plaintiff [sic] care” and “violated plaintiff [sic] care by denying plaintiff of [sic] treatment for headache after plaintiff [sic] fall.”1 The subjective component of Eighth-Amendment claims “is meant to prevent the con-stitutionalization of medical malpractice claims,” Dominguez v. Correctional Med. Servs., 555 F.3d 543, 550 (6th Cir.2009) (internal quotation marks and citation omitted), and Barnett alleges no facts suggesting that Terrie’s incorrect administration of Dilantin was anything other than negligent. It thus constituted medical malpractice at most and cannot constitute an Eighth-Amendment violation. See id.
However, Barnett’s claim that Terrie abandoned him after his fall without providing him with any treatment does state a plausible claim for relief under the Eighth Amendment. Terrie’s alleged presence at the fall and subsequent departure satisfy the subjective requirement. See Blackmore, 390 F.3d at 895-96. And the fact that Barnett, a pro se non-lawyer, titles many of his claims “medical negligence” is immaterial, for a plaintiff pleads facts, not legal claims. See Iqbal, 129 S.Ct. at 1949. It is our job to place those facts into the corresponding legal boxes. See id.
As for the other component of an Eighth-Amendment claim, head injuries— especially after as significant a fall as the one Barnett alleges—are sufficiently serious to satisfy the objective requirement. See Talal v. White, 403 F.3d 423, 427 (6th Cir.2005); see also Williams, 631 F.3d at 384 (finding that “coughing and a shortage of oxygen” is adequately serious, and that—in any case—the “de minimus” nature of an injury is an insufficient basis for dismissal of a complaint). In Talal, we found “sinus problems and dizziness” adequate to constitute a serious medical need. 403 F.3d at 427. Here, the headaches and pain caused by the fall are of comparable nature to the injuries alleged in Talal, so we find that Barnett has adequately pled an Eighth-Amendment claim against Terrie. The dismissal of this claim against her was thus in error.
2. Defendant Hicks
Barnett’s allegation against Hicks, the shift officer on duty when Terrie allegedly improperly gave Barnett Dilantin, is that she sent Barnett to the medical unit without an escort. Barnett, however, does not allege facts that would give us any reason to believe Hicks understood the significance of Barnett’s ingestion of Dilan-tin, including any immediate side effects such as dizziness. At most, Hicks’s actions constitute negligence, which is not actionable under the Eighth Amendment. See Blackmore, 390 F.3d at 895. The district court thus properly dismissed Hicks as a party.
*7893. Defendant Cooper
Aside from the 2002-related claims addressed above, Barnett alleges that Cooper, the prison medical director, failed to adequately supervise the nursing staff and did not provide medical treatment after his Dilantin-related fall (that Cooper did “not se[e] to plaintiff getting the proper medical attention and treatment”). Because Barnett does not allege that Cooper took any deliberate action or otherwise involved himself personally in Terrie’s purported actions, the failure-to-supervise claim is not well taken. See Shehee v. Luttrell, 199 F.3d 295, 300 (6th Cir.1999) (requiring “either encourage[ment of] the specific incident of misconduct or in some other way direct[] participation] in it” for supervisory liability under § 1983). However, Barnett’s allegation that Cooper took no action to treat Barnett’s fall-caused head injuries adequately states a claim for relief. Barnett alleges that he made Cooper aware of the injury through the health-service-request and grievance processes, satisfying the subjective requirement. See Blackmore, 390 F.3d at 895-96. And, as explained above, the purported head injuries are sufficiently serious to meet the objective requirement. See Talal, 403 F.3d at 427. Barnett thus sufficiently pled an Eighth-Amendment claim against Cooper, and the dismissal of this claim against Cooper was in error.
4. Defendant Webb
Barnett alleges that Webb violated his rights based on actions taken in 2002 and potential harm caused to others. As explained above, those arguments fail as a matter of law. One allegation remains: an unclear complaint regarding Webb’s purported delay in receiving results from a 2004 tuberculosis test and getting Barnett medication for his disease. This allegation alternates between alleging negligence for incorrectly checking the results of his tuberculosis test and deliberate failure to treat for a period of time. To the extent that Barnett alleges negligence, his claim is not actionable. See Black-more, 390 F.3d at 895. His claim of deliberate delayed failure to treat, meanwhile, does not allege a sufficiently serious consequence of that purported delay to survive dismissal. See id. at 897-98. The district court thus properly dismissed Webb as a party.
5. Defendant Stipanuk
Because they are partially time-barred and partially precluded by standing, Barnett’s allegations against Stipanuk regarding the 2002 diagnosis or counseling regarding tuberculosis must fail. Barnett also alleges, seemingly for the first time on appeal, that Stipanuk is liable for his failure to train and supervise the nurses that Barnett sues. Because Barnett did not advance this argument below, we may not consider this claim. See Varhola v. Doe, 820 F.2d 809, 815 n. 4 (6th Cir.1987). Yet even were we to consider the merits of this argument, Barnett has failed to allege facts that would indicate Stipanuk “either encouraged the specific incident of misconduct or in some other way directly participated in it.” Shehee, 199 F.3d at 300 (internal quotation marks and citation omitted). The district court thus properly dismissed Stipanuk as a party.
6. Defendant Luttrell
Barnett alleges that Luttrell, the Shelby County Sheriff, failed to adequately train and supervise jail employees. However, there is no respondeat superior liability under § 1983, and Barnett does not allege that Luttrell encouraged or participated in any particular unconstitutional action. See id. A failure-to-train claim, meanwhile, is properly directed against the municipality. See Phillips v. Roane Cnty., *790Tenn., 534 F.3d 531, 543-44 (6th Cir.2008). The district court thus properly dismissed Luttrell as a party.
7. Defendants Shelby County and Correctional Medical Services
Barnett argues that Shelby County and CMS failed to train and supervise their employees, but he points to no deliberate action by CMS, see Shehee, 199 F.3d at 300, and does not allege facts indicating a particular municipal policy or custom of deliberate indifference, see Miller v. Sanilac Cnty., 606 F.3d 240, 255 (6th Cir.2010). Barnett thus has not adequately pled these claims, and the district court properly dismissed Shelby County and CMS as defendants.
III.
For the foregoing reasons, we AFFIRM the district court’s dismissal of Barnett’s claims against all defendants but Terrie and Cooper, REVERSE the district court’s dismissal of Barnett’s failure-to-treat claims against Terrie and Cooper, and REMAND for further proceedings consistent with this opinion.
. Barnett alleged below also that the Dilantin caused him a rash, but he seems to have abandoned that claim on appeal, so we do not consider it. See Bickel v. Korean Air Lines Co., 96 F.3d 151, 153 (6th Cir.1996).