I wish I could say something that would help, or some kind of epic advice that would make all this make sense.
Unfortunately, all I can tell you is that I'm in almost the same exact situation, only I'm dating a girl. A girl who's pretty sure she's a lesbian, and could possibly be asexual. So we're both all sorts of confused and terrified and generally screwed up.
If you guys split, is there any way you could at least stay close friends, or would that be too painful? I hope someone else who's wiser or at least better with words than me responds to this, and I seriously hope whichever option you go with works out for you. It's a miserable place to be in, and I'd only wish it on the worst.