Another day, another ancient PTSD question! There are some excellent posts on this in our FAQ. In this thread I discuss the Greek evidence (including Ajax, further down the thread), while /u/kookingpot takes care of the Assyrian material that may or may not indicate post-traumatic stress. For detailed information on the Romans and combat stress see /u/sapere_avde's posts here and here.
It's worth emphasizing that no ancient source can ever be "evidence of PTSD", since the diagnosis can only be made by a mental health professional upon interviewing a patient. This has only been possible since the 1970s because before that time the specific diagnosis did not exist. Since we cannot interview people who are long dead, we cannot reasonably declare that what little we know about them shows that they suffered from PTSD. Any retroactive diagnosis on the basis of our very superficial evidence is going to be very shaky indeed. The best we can say is that some sources show people in ancient times being mentally or physically changed by exposure to extreme danger. Some scholars argue that this is sufficient, because PTSD is a universal aspect of the human condition; others argue that the different conditions of warfare in ancient times would not have produced the same stresses seen in modern warfare, and would therefore produce different mental and physical reactions as well.
As has been said, it's really impossible to point to anything in ancient sources and diagnose it as PTSD.
What can be said is that ancient historians were aware that war had a psychological impact and cited examples of it. Herodotus tells the story of Epizelus, an Athenian, who goes blind and mute after a soldier near him dies. Herodotus notes that Epizelus, himself, was not wounded. I don't cite Herodotus as a factual source (although I give him more credit than many). But he was clearly aware of the concept that war could cause psychological harm which can manifest physically even if he wouldn't have put it that way.
Plutarch says that several soldiers from Syracuse went deaf and mute during the Roman siege.
After the defeat at Carrhae, Plutarch says Crassus refused to come out of his tent. He is described as laying there with his face covered. Even when he should have been out comforting/pumping up the troops.
Tacitus describes a scene after the mutiny against Germanicus. The troops feel so shamed they go out and systematically slay the opposing side. This is more complicated. But we see that the soldiers are acting out in violence based on an emotional/psychological cause. I won't put a modern gloss on it.
I don't think you can point to anything in the ancient sources and say "that is PTSD" but I do think there is quite a bit to suggest that war had a psychological impact on soldiers. It may have manifested itself differently. Societies handled it differently. But it was something they were aware of on some level.
Going away from histories, Ovid wrote in Heroides of a returned soldier in a tavern drawing a map of Troy with spilled wine going over all of the landmarks ("this is the Sigeian territory,/here stood the lofty palace of old Priam,/there the tent of Achilles...’"). Evocative of a man still stuck on the frontlines in his own mind.
As discussed above, I don't think literature is an appropriate place for an historian to definitively state any facts about ancient life (except, perhaps the most broad ones). But I do think you can see reflected the general acknowledgement that war can be brutal and has a deep impact that isn't easily shaken off. We can't diagnose people from the past but we can say that they were human beings who felt as deeply as we do today even if it was expressed in different ways or manifested itself differently. And returning soldiers should know that if Achilles, perhaps the greatest soldier in literature, can feel grief, anger, guilt, and rage there is certainly no shame or weakness in it.