Search Results: getting mad at boyfriend

So, I was out eating with my boyfriend & he was trying to show my something on his phone when suddenly a snapchat message appears from (i'll change the name for anon purposes) Marla. He swipes it away quickly, and I ask, "who was that, whats her name?". He says just some chick, and then he tries changing the subject really fast. We get into the car, and I ask again, "so how do you know eachother, AND WHATS HER NAME?" He insists its just some girl he knows (and that he ONLY has her on snap), and after a while he says her name is Melissa. A lie. I let it go, but the next day I look up the name I saw (Marla) on facebook & instagram. I see he's consistently liking pics, including bikini pics. I ask him again saying, "you obviously know her, and you lied about her name, WHO IS SHE?" he says he has a class with her, so he talks with her through only snap (which is sketch, cus everything dissapears.
Okay, so skip ahead a bit, we're at his house and we took a nap, but I wake up first. I see he had a message from Marla through snap and text, and I know it was wrong, but I was anxious, so I look through his phone. I find out they had been going out a LOT (which he never mentioned), he would call her adorable, offer to buy her food a lot, and that they were planning on taking more classes together next semester. I got mad, because he is the most JEALOUS person I have ever been with, yet he's getting THIS close with another girl.
I confront him about it and get mad that I don't trust him. We almost broke up over it.
After all of this, he still insists on liking her photos and STILL ended up taking another class with her.
I just feel disrespected. How would you all feel?

Well this guy and me have been hooking up he’s always giving mixed signals telling me he wants to be with me and me saying I do to. Him basically saying he loved me. He has serious trust issues and emotionally unavailable af. But despite that I see he’s struggling hard. He likes me I’m sure he does but I guess not enough. We work together md he decide to invite one of the girls he talks to visit him at work even though I didn’t know he talked to other girls. And he was smiling at me like it was funny. He always tries to make me jealous. So I went up to him after that and started getting emotional and said if he didn’t like me he didn’t have to lie and I started crying he called after my name and I ran in the bathroom. Me he came vigorously knocking on the door all concerned. Then I just was kinda mean to him and h said we aren’t going out which I cmt be mad he talks to her. That broke my heart because I swore he said he wanted to date me. He tried getting my attention but I didn’t give it to him. How should I act when I see him tomorrow? I mean icant be too mad because he’s right he isn’t my boyfriend but to do it in my face is mean.