Should I break up with him?

I haven been dating my boyfriend for almost two years. The whole time it has been nothing but great! We have barely ever fought up until about a month ago. At first he seemed really emotionally distant and would treat me only like a friend in front of his friends. Then I found out that he was talking to another girl at his school and even hung out with her! I found this out through someone else which really bothers me that he didn't even have the common decency to tell me what was going on. Anyways, he changed his story about 5 or 6 times about what they did when they hung out and for how long. I then asked him to delete her off of everything (fb, insta, snapchat, contacts) and after about 4 days he still didn't do it and wouldn't let me see his phone. Idk whether or not to trust him anymore and I'm not sure if I should stay with him. I love him but idk if he will give the effort to fix it. Please please help!