How do I deal with her issues with me?

Unfortunately, jealousy doesn't look good on anyone, and this is a clic case of jealousy. If she were a level-headed person, I'd say sit her down, and ask her to tell you how she feels. Then say, look, this is not a competition, and tell her why she's great. Make her believe you. Then see how things go from there. Wouldn't spend too much time on it, though. You don't need the drama and negativity in your life.