If he's betrayed your trust then you have to decide if you want to stay with him. Trust is something that you need for a happy relationship. You don't trust somebody just a little bit you either trust them or you don't.
Doubting everything is not a happy situation to be in, a relationship should make you feel happy but this one sounds as though it's causing your more grief than happiness. Do you want to continue like this? Be honest with yourself even though the answer may hurt.