OP you have your child to care for,and your Degree to complete. This man has been emotionally and physically abusive to you. Going NC is bloody hard - I've been there. But really if you don't look after yourselfan your worth, your self-esteem nobody else is going to do it for you.
Your ex sounds like a pain, tbh. He hurt you, said it was a 'game?!'. If he sees he can still get you back after abusing you emoitionally and physiically, then what message will that send to him regarding how you see yourself and your worth? Do you really think, he's going to treat you with love and respect?
Unfortunately we can't turn love off like a switch, nor always face fact that not everybody or everything we want in this life is good for us. But at times, we must. Too many women wasting years on useless men, blocking their own opportunities, hopes, dreams, goals for the sake of this man they absolutely MUST have at all costs; as if despite his abusive behaviour, they will somehow wither away and die for lack of him. Yet in reality a strong possibility is years of turmoil then regrets in life, looking back down the years thinking 'if only I'd stayed away from him'.
Not trying to take away how you must feel. Just hoping you see that a partner's supposed to enhance your life, not give you so many reasons for despair of relationship that you can fill pages with it! Cherish yourself, your DC, get that degree, re-establish links with friends. Forget about internet dating and men for a while. You'll survive. Make a life for yourself, don't let your ex waste your good years, and you'll eventually find a good decent man to share life with you. Good luck