The first criterion for having PTSD is obviously experiencing some kind of trauma, specifically in situations dealing with death or the possibility of death, injury, or sexual violence. Tony obviously meets this criterion.
Next, to be diagnosed with PTSD, someone needs to experience intrusive memories or dreams, flashbacks, or psychological or physical distress at something that reminds that person of the traumatic event. The movie never shows Tony experiencing any dreams or flashbacks concerning his trauma, and we don’t know if he had intrusive memories of the event. If he had any psychological or physical distress at reminders, they were not visible during the movie.
Next people with PTSD avoid anything that reminds them of the trauma, either memories, thoughts, or feelings concerning the event, or environmental reminders. Tony doesn’t seem to meet this criterion since he talks about his traumatic experience willingly and even goes back to the area to save the town from the Ten Rings.
Next, a person has to show negative changes in thoughts and mood in at least two separate areas. Perhaps a person is unable to remember important parts of the trauma. They may develop a negative worldview. Tony seems to become less cynical and optimistic after he returns, stopping weapon production at his company and focusing on philanthropic pursuits. Victims of a traumatic event with PTSD may blame themselves or others who are not actually the perpetrators. They may exhibit a negative emotional state and have an inability to experience positive emotions.
Throughout the movie after his trauma, Tony does frequently become upset, but he does so in reasonable situations. He also continues to experience positive emotions, like his feelings toward Pepper or even just exhilaration while flying. People may show less of an interest or participation in activities they used to enjoy, or feel detached from significant friends and family. If just looking at Tony’s behavior during the first Iron Man film, I don’t believe he shows any of these symptoms.
Finally, criteria include showing changes in arousal reactivity, in at least two separate areas. People could show irritable behavior and angry outbursts. Again, Tony does become upset in situations, but his responses are reasonable. People could engage in reckless or self-destructive behavior, which Tony absolutely does by becoming Iron Man and fighting the Ten Rings.
Another possible symptom is hypervigilance. Tony does show heightened vigilance as a superhero, but his vigilance doesn’t seem outside the norm of any other kind of hero in dangerous situations, like a police officer or firefighter. Related to hypervigilance is an exaggerated startle response. Tony never overreacts to surprises, but he does remind Pepper not to sneak up on him. PTSD symptoms can include difficulty with concentration. Tony has no problems concentrating on his projects. Last is sign of sleep disturbance, which the movie does not explicitly show.
The last three criteria are more technicalities. If someone has PTSD, they experience symptoms longer than 1 month. Even if Tony met all the criteria for this diagnosis, I’m not sure how long the movie spans. These symptoms also have to illustrate clinically significant distress and cannot be somehow due to substance use or a medical condition. If Tony does have any of the above symptoms indicating PTSD, a clinician would have to determine that they are not a side effect of the arc reactor in his heart.