Is this cheating?

I 23F have been married to my husband 29M for 2years. We stay with his parents and recently I had a huge fight with my mother in law. It was just her screaming at me and calling me names. So after this happened the third time I left and told my husband will come back when he decides to move. I came back yesterday after a week and he promised me that we would move. But after I came back I sensed that something was wrong he had changed his profile picture with me and had also changed his phone password. Today I confronted him and after a lot of back on forth he confessed that he was in fact cheating on me but it wasn’t physical. He was just flirting with girls online because that made him feel good about himself. He has done this in the past with his ex girlfriend but justified by saying that it was a long distance and needed validation. I am heartbroken because I have loved this guy with all my heart and have always cared for him. And he on the other hand has been emotionally shut after the marriage and his parents have been terrible to me. He is asking for another chance and wants me to forgive him. He says that he has realised his mistake and will fix himself. I wanted to read the messages but he deleted it in front of me and would not let me read it but kept saying that it was just online flirting and nothing else. It’s hard for me to believe. What should I do? Should I give him another chance and move to a new city and take fresh start? Or should I leave him