Have you spoken about it with your therapist at length? Because it occurs to me that saying you perceive it as being your identity could indicate a few different things. Identity itself is a pretty loaded and somewhat abstract concept.

It's not for me to say, but perhaps you are talking about finding symptoms so overwhelming that they invade your thought process during interaction with others and don't allow core elements of your identity to shine through. Or, saying that you see it as your identity could also refer to the way in which others associate you with your PTSD, and don't see beyond it. I would certainly encourage you to discuss it further with a trusted confidante such as a therapist since while issues of identity can be difficult to deal with, they are a treasure trove of personal insight and growth.