Cheating

I have been married for close to 5 months now and my husband, for the past two or three months, has been accusing me of cheating on him.  I love my husband- we live together, work together...literally do everything together.  I can't, for the life of me, understand why he'd accuse me of cheating.  He doesn't like me going to the store alone.  He always has to tag along and if he doesn't tag along he questions me so much or will say "you can go alone because I trust you".  He does not trust me but I am completely loyal.  
I get so angry and yell and curse at him.  I don't want him touching me in any way when he accuses me of cheating.  Now, I know I shouldn't withhold my body from him but I can't bring myself to do anything with him. Not even kiss.  
I know that he isn't cheating on me, but before we got married he was in a relationship and left her for me.  It wasn't a serious relationship and it was supposedly "open", but maybe this is my karma for breaking them up... I don't know.  I'm just so hurt and upset. I don't know if I want advice or if I just needed to vent.   Probably both.