I’m sorry to be the one to tell you but there is no way you can make him understand he can trust you. As you pointed out, you’ve done nothing to earn his mistrust. You even moved far from home, friends and family to be with him but that isn’t enough. His anxiety about what you are doing isn’t your fault. It is coming from somewhere inside him.
I worry that his level of suspicion and his attempts to control you as the solution to his problem will only get worse. In cases like this, it often does. He is already isolating you from others and setting up rules for you that are different from the rules he sets for himself. He is already manipulating you and limiting even what you can talk about! No wonder your sex drive has gone downhill. Your whole system is telling you that something is very, very wrong.
Your boyfriend needs to do some personal therapeutic work before he is fit to be a partner. You don’t want to spend the rest of your life walking on eggshells to keep him from being upset. If he is honest with himself, he doesn’t really want the woman he loves to be afraid of him and to be unable to live a normal life because of his anxiety.
I suggest you take a break and go home. Give him time to get some therapy and to show you that he can love you and trust you and encourage you to spread your wings instead of clipping them. Only then does it make sense to go forward with the relationship.
I wish you well.