This is why I am not friends with too many girls. So much drama. Well, first of all, stop telling her she is being stupid. These are her emotions and she cannot control them, whether they are valid or not. Try to put yourself in her shoes for a minute. She has low self esteem, her close friends have hurt her before, and she now likes a new boy. Imagine this situation happened to you. Since you were drinking, I am to assume she was as well. You know that you don't have the most rational thoughts when drinking, so she probably over exaggerated that evening.
At this point, I think the best you can do, is call/write and apologize for what happened. DO NOT apologize for anything you did, because from what you are saying, you handled everything properly, but apologize for the misunderstanding. Explain that you have no interest in this boy, and let her know that you are actually interested in someone else (even if she already knows that). Let her know that her friendship is very important to you and its been a while since you have connected with someone like you have with her, and don't want to lose her friendship. That is really all you can do. After that, its up to her. I hope she does realize that you did not do anything wrong, but you never know. If she does not speak with you after that though, know that you have done all you can,and that this might just be too tough a situation for her to continue dealing with.