OP: Are you saying she is on her period now or are you saying that she was on the last day of her period when this happened?
Anyway, regardless. Get a rubber on or get her on birth control pills. If you don't you will have this anxiety every time you have sex with her. You need to practice safe sex. It's the grown up and responsible thing to be doing, particularly with this girl because she makes little sense in her reasons for not doing certain things and you don't seem to have your sex life with her under any kind of control. She's the type that will trick you into being a father (whether it be intentionally or because of her crazy far out emotional ideas of what she should and shouldn't be doing. Look after yourself. If you were my son I'd be telling you to NEVER have sex with her without a condom even if she said she was on the pill.
Good luck, let us know if she's having a hysterical pregnancy or a real one.