My first problem with the ladies post

Ok, here's the background. About a month ago this girl and I were drinking and hanging out, and she mentioned that her grandma was coming to visit, and she needed to pretend to have a boyfriend to keep her grandma from yelling at her. I volunteered, and she accepted. She left soon after, and I sent her a blacked-out drunken email telling her we should go on a "fake-date," since I had to be her fake boyfriend.

A week goes by, and she asks "so are you still interested in that fake-date?" I assume she means the fake-boyfriend thing, so I say yes, and then find the drunken email, so I assume she meant that offer. We go to see a concert, but we're with my roommates, so nothing happens.

A few weeks later, I ask her if she'd like to go to a formal with me. She says, "Well, see, I already have a back-up date to the formal, so it depends if I like you more than I like him. And he's gay." My friend points out that I am not gay, and she decides to go with me, making sure to tell me how disappointed her gay friend is.

This girl and I are friends, I see her in class all the time, etc. etc. I'm not good with women, and I'm pretty sure I [censored] this up good. Is the situation salvageable, or should I just go, get it over with, and write her off as datable?