She is pregnant, i AM SURE its not mine, but she claims it is! please help!?

A girl who i met a few times came over to my house when my parents were away(im 19)and her and i decided to have . I put a condom on, we had and when i turned the lights on i was covered in blood. It turns out she had started her period that morning and didnt want to tell me. After that i was disgusted and mad at her so i very rudely told her to leave. A week and a half later she calls me claiming to be pregnant with my child. I deny it, but then after a trip to the doctor i find out she really is pregnant. i am positive that a girl cannot get pregnant while she is on her period, especially if i had a condom on. I think she is trying to use me cause for someone my age i make good money, come from a good family, and live a very upper cl lifestyle. I have a feeling she is trying to get money or support from me by claiming im the father but in reality some other guy got her pregnant. How do i deal with this? and, she is threatening to tell my parents, what do i say if she does?