I'm confused. Is she jealous of you or are you jealous of her? Either way, it doesn't matter. If she owes you money, then you're perfectly okay to ask her about this. "Hey, Susan, I was just wondering about that $10 that I loaned you a couple of weeks ago. My mom wanted to know when you could pay me back."
Don't bring up all the new stuff that she has - it could be that her mom is buying her all that. If she blows you off, saying that she doesn't have the money, let it go. It's not worth the trouble. Just know that if you "loan" her any money, she won't pay you back.
Just be an acquaintance to her for the sake of working on the project together. You don't need to share secrets for that. You just have to learn how to work together and get along. You have a shared goal - getting the work done. So concentrate on that and let the other stuff go.