Boyfriend Has feelings for ex?

Hey everyone. I am 20 years old and I'm currently dating a wonderful guy. We have been dating for 5 months. I have been trying my best to be there for him and let him know that I really care about him. I let him know what about him I like as well. We hang out a lot. In turn, I think I may be falling for him even more and my feelings seem to be growing for him. However, the problem is his ex. Before me, he was in a 2-year relationship. He told me that he still has feelings for her and its nearly been a year since their break up but he says he likes me a lot and cares about me. It still hurts. I'm disappointed because I have no feelings for anyone else and I think I may be starting to love him. Do I have the right to feel the way I feel?