What should I do? Confront him?

[Curious]

I've been dating a guy for almost 2 yrs. At the beginning I wasn't jealous at all. My boyfriend is very attractive and always have girls around him. At first this never bother me and I was happy my boyfriend is attractive. Although like a year ago he was texting his ex and in a random conversation he said I wasn't the jealous type like his ex and that it is good I never read his messages. Anyways the tone and randomness made me very curious and I read his text messages one time and saw he texted her and was kinda flirty. I told him what I did and ask him if he had any feelings for her. He said no, and I said ok. He ask me if I was ok with it and I said yes. A few days later he told me things got awkward because she told him she wanted him back. I told him to stop texting with her. And he did. Until like 3 months later. He didn't told me and he even gave her a birthday card. Later she texted him how she stll dreams of him and he told me. He told her to stop texting but she kept at it. So one day I just text her and told her to stop begging him. She replied that he is a good man and wouldn't brake my heart but that he still loves her. My bf said he couldn't believe what she said and said no. I believe is true because I wanted to break up with him and he please don't. A few days after that she texted again saying she was sorry to him because she broke his heart. And he ask me what he should reply and I said nothing. (Which I think is the worst text ever).

Anyways we never had problems again. However recently he said something odd about how I cant read his messages. I was in Facebook and it was in his page and he thought I was sign in with his account. But I wasn't and never look at it even though it is sign in my computer. Then he said alright. This made me feel uneasy and I check his fb but nothing was there. I felt guilty but I don't think its a big deal. Anywyas I feel like he was hiding something. So later the next day I read his messages...

This time he was texting his coworker. She actually got fired a few weeks ago. She rides a motorcycle and one time she ask him for a ride and he gave him one. Kinda bother me, I think I felt a little jealous. Anyways they have been texting for a while. Random crap. He texted "Don't think too much about me" And she said I'll try. He had told me before that she likes him so I think that was weird. I trust my bf he even proposed to me but I said no because it was too soon. I think he is just a flirt and maybe part of him feels like I might end up leaving him so he surrounds himself with girls..

My question is, do you think I should confront him that I read his messages and they are not appropriate or should I completely trust him, and say nothing. I don't want to be the jealous girlfriend but I feel that since he was talking to his ex, the trust I had declined.