Worried or not? He Lied about ex girlfriend

Hi,

So here is the scoop. We have been together for 2 years. The first year I tried to be okay with my guy being friends with his ex. He would text her multiple times a week and Snapchat daily. After a while it started to bother me and told him that I wasn't very comfortable with it. He was super defensive and said they were only friends. Then he started to hide their conversations from me and at that point I asked him to break ties or else I was going to leave. Since then I've caught him lying about talking to her about 5 times. And each time he says he is done talking to her. Things have been okay for a while but he still has an old note from her and keeps old Facebook photos of them (keep in mind he asked me to delete all my old photos of myself and my ex). I feel like i am in constant competition with her even though she lives hours away. Even his family has said comments to me about them being friends still in regards to him making a future with me and not her. They don't get why he still keeps in contact. I'm not the controlling or crazy girl type at all, but this whole situation makes me feel that way. Am I wrong for asking him to cut ties? Should I be worried?