Unless you've actually cheated at some point, the way he's treating you is ridiculous, and in no way normal. Unless you've given him reason, you should not have to "deserve" his trust, you should have it. I don't care about whatever may have happened to him in the past, issues he may have had with anyone else should not be your issues. Without trust, you cannot have a happy, healthy LDR, it's the most important component, and no one should ever try getting into an LDR with someone they don't trust.
You need to ask yourself why you're willing to put up with this. If you've done nothing wrong, you don't deserve this crap, it's not how a normal relationship works. If you want to be with this guy, it's time to put your foot down and demand trust and better treatment, if he can't, trust me, he isn't worth your time.