My boyfriend always thinks I'm cheating

I've been in a relationship for a year and a half with a man that I also have a child with I was in a very toxic abusive relationship before him and I was also addicted heavily on drugs but I gave up the drugs and I left the toxic relationship being with my new partner I have a lot of Happy times a lot but I'm constantly accused of cheating sneaking out of the house my body doesn't feel the same every time and so on I've never cheated on him not even the piece of crap boyfriend I was with before I guess it's insecurities with my current partner but I don't know what to do I'm at a loss I try it all the time to show him that I've only for him and it's never quite enough I caught him liking and talking to other people on sites that were inappropriate he said he never met up with those people but it still hurt just as bad I constantly try to provide proof for him every time he steps out of the house so that he could say I'm not doing anything wrong but he always finds small things to say that I am for instance getting my period unfortunately I'm on a birth control that messed it all up and I have gotten it at a random time once and you thought that it was because I was with someone else my bed is on the floor with two twin size mattresses underneath a king bed I get on and off it throughout the day with my infant child and I guess it slides a little bit but he thinks other things I guess he also says that my body is different sometimes when we're intimate and I really don't know why but I definitely wasn't with someone else I'm home all day and I'm trying to show him that I'm here for him and he still doesn't understand I gave up drugs heavy drugs I gave up injecting drugs and my family who are all on drugs to show him that may be I'm worth it it's still not enough he thinks I sneak out in the middle of the night even though he gets up throughout the night I've always been told that somebody that's doing this would accuse their partner of it I just hope that's not it but what do I do I don't want to leave him I want to help show him that that's not the person I am but I don't know what else to do