Hi PS,
I'm from the United States (I don't know if that matters, but I don't know where you're from), and in the city where I live, "being in a relationship" usually implies a sexual component. At least to me. I can't speak for everyone!

It varies, though. There are plenty of folks who have romantic relationships and don't do anything more than kiss until they're married. It's all about personal preference.
I'm not sure why you would
only be attracted to the gorgeous ones. I mean, it's common for men to like the really pretty ones best, since men are (statistically) visually turned on.
Are you setting your standards that high
intentionally? A couple possibilities for that could be "She's gorgeous, so the fact that she's with me validates me." Or, it could be that you're protecting yourself from rejection. Some folks set the bar high so that it doesn't hurt as bad when the girl says "no." Kind of like, "Oh, no big deal--I expected that." So, are you sure that you're not setting yourself an intentionally unreachable goal? Maybe you've forced yourself, by this point, to not consciously consider other women attractive--because of your no-premarital-sex lifestyle? But the really pretty ones still get through that wall you've built?
The thing I notice most is that you're letting women choose you, and not the other way around. And I don't think that it's simply because you're scared. I think you're intentionally doing that, and for some reason I want to say that you're trying to avoid responsibility for your thoughts or actions. I have NO idea where I'm getting this, so I could be completely off.
I think that another component is that you're not sure what you can offer...so make a list.

--Frayed
Do not take my advice before talking to your doctor/counselor/other professional. Depending on where you live, you may be able to find free, confidential care. Most importantly, sometimes your shrink can be wrong. Get a second opinion.