I'm so angry with him that I want to hurt him.
I'm sorry you feel that way, why do you want to hurt him?
He's started dating another woman and I'm so mad at him.
It sounds like you still have feelings for him, but you can't hurt him because of it. Instead of focusing on him, try to find someone new for yourself.
I can't believe he's moved on so fast, after what he did to me it's not fair.
It sounds like your relationship ended very badly and I'm sorry about that. Holding on to your anger towards him is not healthy. You have to move on and try to find happiness.