First, kudos to RM for giving the important info about HPV. That is something you should digest carefully, and also, talk to your doctor about the HPV vaccine and whether that is appropriate for you.
Second, should you rat on the blabbermouth? Well, it seems clear to me that your girl, let's call her George, is using safe practices with respect to her STD. The other girl, let's call her Bess, is broadcasting information to people who are not sexually involved with George about things they only need to be know if they are sexually involved with George. So, basically, Bess is being a douche.
Do you tell George that Bess is being a douche? That depends upon whether you care about George and how much you want to be friends with Bess. If you care about George enough, you may want to let her know that her douche bag friend Bess is treating her like a leper. If you want to stay friends with Bess then you may not want to characterize her as a complete waste of space and a, did I mention, douche bag.
When I was a kid and we played Nancy Drew, abolutely no one wanted to be Bess. Ever.