Should we break up?

My current boyfriend and I have been dating for about 3 months right now, but he constantly talks about his ex. He also spent the night at a girls house, because they were going to a convention the next day, and it was for “transportation purposes”. They slept in the same room. We are both 15 and abstinent, so I know they didn’t have sex, but I’m still worried about other things possibly happening. We have talked through these issues, and he has promised me that he will work harder to be more available and to no longer do things such as this. However it has been almost a week and nothing has changed. I want to give him time to improve, but at the same time I don’t want to let myself get treated this way. I feel as if I’m constantly being compared to his ex, and he’s rejected all of my attempts to go on dates so far (3 attempts). Should I continue with this relationship? I still really like him, but I don’t want to subject myself to emotional pain.