Run, don’t walk, away from this relationship. Yes, it’s wrong. It was wrong of him to cheat on you and it’s wrong for you to participate in his cheating on another young woman. This young man has told you he is a sociopath. I don’t know if that is entirely true, but it is true that he is acting like a potential abuser. He makes you dependent, abandons you, begs forgiveness, then forces you — with the threat of violence just barely under the surface. Yikes! Get away.
You are not a “bad” person. You have been manipulated and psychologically abused. You do need to see a therapist to help you sort out your feelings and to get over the dependency. Don’t let a lack of funds stand in the way. If there is a counselor at school, ask to see her or him. If that person can’t do some counseling with you, ask for information about free or low cost counseling for teens in your area. Many communities have such services. If your parents have any kind of health insurance, they should explore whether it will pay for some help for you.
I’m so sorry that your first experience with love and relationships has been such a bad one. I hope you will get the help you need so that you can move on and find someone who will love you and cherish you as you deserve.
I wish you well.