What do I do to fix my marriage?

 My husband and I have been married for 31 years, together 36 years. I am madly in love with him still.  But lately things have been uncomfortable.  I really don't think he likes me anymore.  The last couple of weeks he cringes when I touch him.  I was in a bad car accident on Monday and when he came to pick me up I hugged him and he flinched away from me.  If I touch him in any way he gives me a dirty look.  I don't know how to fix this.  I don't know if it can be fixed.

Several years ago he accused me of cheating on him.  Let me be clear...I have Never Ever cheated on him.  He told me someone else told him that I cheated.  He states that person showed him proof.  He has never shown me what this person showed him.  But he believes this person over me.  His past relationships, all the women cheated on him.  So therefore...I must have cheated on him.  I haven't.  But he is convinced I have.  We have had several fights over this and he just won't believe me.  I'm sure that this is part of why he hates me.

So how can I fix this.  I have suggested couples therapy.  He said I should get therapy.  I'm sitting here at 1 am writing this because I can't sleep for worrying about this.  I love this man with all my heart, but he is breaking it bit by bit. I'm afraid to bring up anything because it always gets turned around to be my fault.  I am starting a fight. I am causing trouble.  I am blaming him for things that are all in my head. I always wind up apologizing and backing down. 

We are more like roommates than a married couple.  We still sleep in the same bed, but do not touch.  I just don't know what to do or how to fix this.