There are a variety of coping strategies you can try, and as others have said, it's not entirely possible at this point in any case to firmly diagnose that someone is transsexual (in fact there's at least some controversy about the term itself, for some transgendered folks). I doubt there are any of us who would choose this, and in my therapy comments have been made about my obsessiveness, never a formal diagnosis of OCD, though.
I've gone for years avoiding transition based on several different rationales, and some of my coping strategies more or less worked for a time. The feelings haven't gone away, though, and I'm skeptical about describing them as obsessive thoughts when it feels more like knowing what I am inside, and being conflicted about the best ways of externalizing that, and finding ways of being seen by others without putting myself at dangerous risk.
I can't say my own approach would work for you, or even that it was a good course for me. It just happens to be what I've done (and not done) with my life. I'd suggest trying to map out what it is that you feel is lacking, and what are the possible actions you could take that might make that better. It could be something like androgyny, or something else. But it sounds to me from your description of the drag event, that for you, it's not about a performance, but more a desire to express something within yourself.
I don't know -- you haven't said -- what all your feelings are, so I'm hesitant to suggest anything more than this.
