Is it normal that i am crushing on her now?

A few weeks ago I went to a party and got pretty smashed. Later in the evening, 2 friends of mine who happen to be dating pulled me into a bedroom with the mindset to seduce me. I'm pretty open-minded, would've been cool with the threesome (I'm a pretty chatty drunk though unfortunately, and wound up pouring all my secrets out instead of being involved in a 3-way), whatever. Not an issue.
The whole talking thing actually made the situation a lot more complicated. She handled it beautifully, was super nice and understanding to me, and in the end I wound up feeling all warm and fuzzy - but maybe that was just the alcohol... Her kindness to me though is something that I think is really making me hooked on her.
My problem is that now I am finding that I have a great big crush on the girl. We have a really bizarre history, she is at odds constantly with my best friend, and we both have previously screwed one another over a fair number of times. This seems like a 1-time-only thing. I'm furious with myself for missing my chance with her though, and now I'm finding that I can't stop thinking about her and the situation.

Basically, I'm crushing on one of my friends and have no idea how to handle it. Because of our past differences, I feel weird about soberly approaching her about anything, and I have no idea what I'd even say anyways.

Is this even normal?