Most Helpful Guy
Domestic abuse typically goes through stages, one of which is jealousy, controlling behavior. Do I have to go through the other stages? NOT saying he will end up physically abusing you (and hopefully he won't) but that behavior is not normal.
Many times the guy yapping the loudest about his woman cheating is a cheater himself. The ol deflect/project manipulate tactic.
Most Helpful Girl
He has trust issues which results in controlling behavior - a major red flag... I dont know how long you two have been together and how long this has been going on, but first talk with him about it. If you can't solve the problem together, I would consider leaving him.