Has Harry Potter PTSD

Does Tony Stark really have PTSD or just afraid of the things to come?

Since Tony is never really dealt with in the film, there is no straightforward yes / no answer to it. You can read the DSM's criteria for PTSD here and see that Tony definitely shows a lot of the symptoms of PTSD during the movie. This article (despite frequent formatting issues) does a great job of discussing Tony's arc through the 4 films and their relationship to PTSD. The article does not attempt to diagnose Tony directly, but makes some good points:

In fictional patients, labels can normalize the experience of disorders and destigmatize mental illness. However, the brilliance of the third installment of Iron Man stems from the complexity of Tony's psychology. Iron Man doesn't work absolutely either. The film appears to be purposely portraying mental illness with an elaborate level of ambiguity and dimension, emphasizing the realistic point that the course of mental illness has no definite causes, cures, beginnings or ends.

This praise for a complex, realistic portrayal of Tony's problems parallels the praise I have elsewhere for the Inclusion of mental health problems through Iron man 3 have seen. For example:

It was amazing to see the world's number one movie, a huge summer blockbuster, deal so calmly and rationally with mental illness. Everyone in Tony's life knows he's sick and they try to help him. He does what he can to alleviate his illness (although as far as I can tell he is never treated) and to get better. Nobody questions their ability to be a superhero or a genius or even a functioning person. The illness itself has been shown to be life-threatening and scary to him, but not so exaggerated that it was a cartoon.

Regardless of whether he is specially at Suffering from PTSD or not, he has some serious mental health issues, and one of the arcs of the film is that he deals with it. The way he speaks makes it clear, in my opinion, that his problems are due to what was going on in New York while The avengers happened, rather than the future threat that we know will come from Thanos. Tony, telling Pepper he couldn't sleep because of an impending threat, sounded like a distraction to me. He knows that thinking about and talking about New York is a trigger for his anxiety attacks by saying that he builds the suits for a vague future threat that he circumvents to discuss New York and the pain that comes with it .