Sounds like her mom is trying to scare her. The shots will prevent certain causes of HPV that may cause cervical cancer. You can still get cervical cancer without having HPV, but the percentage of non-HPV cancer is lower than cervical cancer caused by HPV.
Each time you have sex your risk of cervical cancer does not increase. If you have already had unprotected sex with your girlfriend and either one of you had high risk HPV, you have passed it to each other. Once you get HPV, no shot in the world is going to prevent it. However, having HPV does not automatically mean you'll get cervical cancer either.
Wear condoms if you are concerned. They protect against STDs and pregnancy. Its the best of both worlds!