Suspicious boyfriend and I broke up but still live together?

My boyfriend of three and a half years just broke up today, but we live together in the city and both go to college and neither have the time or money right now to move out right away. Often when I walk over to his computer, he closes out of IMs with girls he talks to online and refuses to open them with me standing near him. I caught him a year ago flirting and making ual jokes with a stranger online, and we nearly broke up over it. He knows I hate when he hides stuff, but he still does it, which makes me suspicious. A week ago, he did the quick closing out of IMs again, and kept denying he was talking with the girl I swore who's screen name I saw. We fought about it and again almost broke up, but I let it go, even though its hard to trust him. Then, today, he did it again! I couldn't see who he was talking to, but from far away I saw him typing to someone online. I asked him what he was doing, he said nothing, so I said don't minimize anything. He instantly turns and quickly minimizes the IM. When I got near him, I asked him who he was talking to, and he lied saying he wasn't even online! Then, right in front of me, he right clicks the minimized screen and closes it out. I'm so suspicious and can't trust him at all, and in his argument he slipped and admitted he was talking to the girl he denied IMing a week ago! This, plus the fact he said he was voicing with girls online while I was on vacation for 4 days, and the fact that he never tries anything physical with me EVER anymore, makes me think he's cheating. What should I do to get away from him when we're stuck here? Should I forgive him? I just want it to be over!