It may seem a cluster fuck right now but I bet if you could look at it from the outside in you probably could see somethings you might be missing.
The worst thing in my opinion is you lose or change your job. Don't quite your job! It's just the worst I can see from this. All else if fixable even if avoidance is needed and your pride stays hurt.
You sound like a great guy. I think it's great you would try and befriend/date her. You didn't do anything wrong in them regards. I also think it's great you were so considerate to her and respected her feeling like asking for advice from your friend(s), having a heart, caring about her and having a conscious about it all. That to me is great and them attributes will be put to good use someday.
Since you were not privy to what was or is going on in her head and details about her relationship..... that screwed things up. She needed that friend you were to her that night and then for her it got weird. Reason I say that....
You said you were not even sure you both were friends. You both went out and she was willing to be friends.... or was she?
A huge learning experience you have on your hands. Try and think about it like that.