No, your girlfriend not right to rip up your stuff. If I dated a guy who did this, he'd be out the door. This woman has major jealousy issues.
You should totally be allowed to have mementos from your past, although tucking them away discreetly would be my suggestion as well. As long as you're not taking out your old first date movie stubs with a googly-eyed look on your face and talking about what a wonderful time you had with your first love, then I don't see a problem.
“Inside every cynical person, there is a disappointed idealist”--George Carlin