Can I press breaking and entering charges against my ex-girlfriend?
Did she break into your place?
No, but she went through my stuff.
If she only went through your things it doesn't sound like breaking and entering. It would be wrong to call the police on your girlfriend for such a small personal matter. Just have a conversation with her about your personal boundaries.
Well I think that's the only way I can make her understand
I don't think that she did anything that could be considered a crime, so pressing charges against her would be a waste of time. If you want to her to stop bothering you, it would be better to just tell her.