Should I be mad about this should I dump her?

Ok so last night I caught her in a chat room trying to flirt and when I confronted her about this she said she was just trying to talk to people that she knows that she is taken I have a feeling this is just gonna end up in her cheating btw I treat this girl good I give her all my love and now I just don't know anymore<\3. Should I be mad and break up with her?