I'm worried that my girlfriend gave her number out at the gym
Why do you think she did that?
I'm worried that she did it because she is a slut.
It's not nice for you to call people slurs, specially your girlfriend. If you think that she really gave her number to other people and cheating with you, then you should talk to her first to make sure that what you're saying is true.
I bet she did and she's an evil evil monster.
If you really think your girlfriend is a monster that can't be trusted, then you should just break up with her. Trust is important in maintaining a healthy relationship, and you both will be better off without each other.