He found out I'd been on dating sites, while I was with him? Need some advice?

My boyfriend and I have been together for 8 and a half months. We've been arguing a lot though, and were talking about maybe breaking up. I decided to go online, and find someone else. I chatted to a few men on several different dating sites, but never met any of them, as I didn't find anyone I was interested in. My boyfriend said he didn't want to break up then, so we didn't. Several weeks ago, my email account was hacked into, and he was helping me contact customer support to get back into it. When we finally got into it, we looked at the emails the hacker had sent, but he then saw emails in my inbox from the dating sites. I didn't notice at first, and went to the toilet. When I came back, he had clicked on them, and logged in, as my password was the same as the email one. I hadn't deactivated the account, because I'd forgotten to, and didn't know if I wanted to. I still had photos up, and information. He was looking at a conversation I had had with someone, which was only on the 12th February. We were arguing ECT at that point, but not broken up or anything. The conversation wasn't very detailed, and was mostly just asking questions about each other ECT, and I had said I was planning on breaking up with my boyfriend. He got really angry and started yelling, and said I had cheated, even though I was only on dating sites! He deactivated the accounts, and deleted my photos of it. He then asked to check my phone, and see if there were any unusual text messages or numbers. There weren't, but he was still suspicious. He kept asking if I loved him at all, and started crying. I apologized and explained that I never meant to hurt him, but he doesn't believe me. He seemed to forget about it after a few hours, and said he loved me and stayed another night. The next day he left really early though, and hasn't spoken to me since. I don't know why, and I'm so confused. I don't know whether going on the dating sites was wrong or not? I thought he was breaking up with me at that point, so I was breaking up with him too. I never expected things to 'work out'. They've fallen apart again though. Help? What should I say? Is he still angry?