Being a somewhat private person about my personal life (I am so!), it would really concern me if someone I knew would act like your friend. For one thing, I don't think I'd consider them a friend for long.
I think you should tell her that you truly don't appreciate her acting that way and that if she continues to behave like that she is giving you no choice but to make sure you never tell her anything confidential again and possibly to break off the friendship.
If all that fails, just make stuff up and tell people!