Is he cheating?

My boyfriend and I are very open about everything that goes on in our lives- inside the relationship and out. He works and I go to school. I used to go through his phone, but not because I didn't trust him or do it because I thought that there was something going on but just because I'm a curious person. He never had shown that it bothered him and when we talked about it he said it was ok. However, I stopped for a little while. But then the other night, we were watching a movie and his phone was in front of me and so I picked it up and before I could even unlock the phone he snatched it from me and I asked why I couldn't look through his phone and he said there was something in there that he didn't want me to see. So I backed off- and didn't think much about it honestly. Then today, I went to bed early because I was tired and haven't been getting a lot of sleep. I woke up in the middle of the night and he was sleeping at the end of the bed so I told him to come lay the right way and stuff and he did and we went back to sleep. Right before my alarm went off I turned over to lay/cuddle with him but as I turned over he turned the other way and his phone wasn't on the charger. So I picked up his phone and looked at the time. I also saw he had a text- no biggie, right? Since his texts show up on his lock screen, I read it and it said "lol so you miss me huh" and it was from his co-worker. I've met her before but don't really know her. After reading that, that's when I unlocked his phone and opened up the texts between them. I didn't get very far before my bf woke up and started freaking out because I was going through his phone and pulled the home screen down and took the phone from me and then asking me why I was going through his phone in the middle of the night. Any thoughts?