^^^He's so smart
I gotta agree with the folks who say don't take the drunken "confession" too seriously. Don't ignore it, but I don't think it's the "run like hell" warning sign others think it is. And the fact that she left her fiance....people change a lot when they get to college. Could be she had "outgrown" the relationship and was just looking for a way out. That doesn't mean her feelings for you aren't genuine, but I would say "proceed with some caution" knowing that this girl has a lot of growing to do.
One of the things you'll see repeated over and over again in Tilted Sexuality is that communication is pretty much the #1 recommended approach to all relationship problems. Talk to her about your concerns. Tell her that you're feeling insecure about the relationship because of distance, flirtation, etc., and see what she has to say. It's best, too, if you can "own" your own emotions - don't make it necessarily about her being too this or too that, just say, I'm feeling this way, I'd like to know how you feel about this and about me.
If you're going to continue a long-distance relationship, I think you have to be willing to trust her and to allow her a bit of harmless flirtation without getting bent out of shape, if flirtation is where it stops. She was fricking engaged in high school, and if you don't want to lose her you may need to be confident enough to let her have a little fun. If you can't handle that, then this might not be the right time for you two to hook up.
Good luck!