in my last relationship, I had this constantly. If he understands your OCD, which, I hope he does, maybe you can talk to him about it? Explain what false memories are, and that you're having problems with them. Keeping it in makes it seem more realistic to yourself. Sometimes, talking about your problems and worries out loud makes you realize how silly they really are!
It's funny, once I was out of my relationship, all my fears about cheating went away! It's just one way OCD can morph, nothing more. Don't give it any more power than that.