My boyfriend always thinks im lying

I have been with my boyfriend for almost a year and we are expecting a baby in january. I used to chat a lot online with friends and I havent in about a year. Since I cant delete my account, he thinks im still talking to them wich I am NOT. I also had a picture of an old friend from australia in a profile and I haven't deleted it, not because I dont want to but because I can't access my account for some reason. Now he thinks that im still chatting with him or what not and I don't know what to do to prove to him im not. I love him so much and I want him to trust me but every so often he assumes im lying. All I do all day is stay @ home and do nothing, I even rejected an invite to a party because a guy I used to see was there. I've even tried to delete my chat accounts so he has nothing to worry about about but since I forgot the password I can't. Also I still speak to my ex (we've been broken up for over 1 1/2 now)he is NOTHING but a friend, we stopped having sex the second we broke up witch was WAY before I met my boyfriend, but he thinks im still seeing him too. I don't know what to do please help me prove to him im faithful.

That may be the problem that you are talking to your ex. That does not sit well with some people. You should plainly ask him what could you do to show him that you are not lying about the chatting. You might also consider introducing him to your ex to kinda show him that hey he is a friend and that you have nothing to hide.