My girlfriend has aids and we had unprotected sex because she said that the birth control protected me, true?

No. Bc does not protect you, only condoms, and getting her viral load to undetectable.
No. The birth control pill, when used correctly, protects against pregnancy. But it provides no protection against sexually transmitted infections for either partner.
Get tested. Birth control pills only prevent pregnancy. The safest way to protect yourself is using condoms correctly each and every time. Get yourself tested asap. Initial HIV infection can just feel like flu, or less. Female to male transmission is very possible, like happened to laker legend magic johnson.