Wow, we're seeming more similar all the time. And I've also been told I might have Asperger's.
We're different in that I really want to be two different people at the same time- I really want to be a girly flirty girl, but at the same time there's a totally opposite part of me. That part is pretty androgynous and is much more like a guy and wants to just talk about philosophy and logic.
So I have an ENFP self

And an INTP self
I was kind of unattractive growing up, and was completely unconfidant until a few years ago. I always thought I was ugly, but I knew there was a pretty person inside waiting to come out. I too had no prom date and had my first kiss/hookup at 19. I had no luck with guys whatsoever aside from occasional hookups until a couple of years ago, and I felt like there was something wrong with me because of it. I've always had guy friends; the difference is that I was ok with the fact that they wanted to do me because I like attention. If you don't, I guess it's hard. I too felt really different from the feeling girls, and I thought no one really understood me. I'm pretty weird. But now guys seem to like me anyway, and I think it's because I have confidence and like myself. I constantly pushed myself to be more social, even though I wasn't good at it and was always making blunders and looking like a fool. I've worked really hard at learning proper social behavior and being able to blend in with normal people. (I still make big mistakes occasionally, but such is life.)
So I can understand where you are coming from. I can understand not liking attention because you don't really know what to do with it, and maybe you don't like that kind of forced social interaction. I can totally understand lacking the ability to form meaningful connections with people, and feeling insecure because you don't have a boyfriend. Hopefully you'll be luckier than I was and get one before you are 26.
Anyway, this has been my experience, since the OP asked for it. I constantly tried to improve myself and do everything within my power to change my situation, and so I worked a lot on confidence issues and intimacy issues (I think you also mentioned intimacy issues in the opening post, and I have a theory that INTP girls tend to have these). I notice looking back that my luck with people was directly related to my relationship with myself, my level of confidence, and my level of comfort with intimacy. I used to think I was confident, but I wasn't really. It can be a hard thing to really know. Finally, at 26 I got a boyfriend, I have cool friends who understand me, and I have fantastic luck with people. And somewhere along the line I decided I was in fact very attractive and other people started thinking so as well. (In your case it'll probably look like you enjoying being attractive and attracting the right kind of attention.)
Edit: one more thing, it's totally ok for you to think you are attractive and like it; telling people about it is another thing, but I assume you only mention it irl when it's relevant to the conversation. You're right, it's kind of true that it's best to just not mention it unless it's like "we're both so pretty" so people don't think you are implying that they are not attractive and stuff. Or compliment other people a lot. I dunno. Somehow I've been able to do it and people don't get a conceited vibe from me, unless people on here have and they're just too polite to say so. My feeling is that it's best to just think about it like everyone is beautiful in their own way, like an artist views the world. (And there is objective and subjective beauty, and subjective beauty has more to do with whether someone is attracted to you rather than thinking you are attractive my objective standards.) I'm rambling, but I wanted to attempt to clarify the situation.