Is this something to break-up over with?

If he has ignored you for a week, then it's safe to assume you are already broken up. That goes beyond needing to cool off or even retaliation, he is done. If he isn't, then it's still inexcusable and you still need to break up. Healthy couples talk out their problems together. Communication was already terrible between you two, screaming arguments are not normal or ok. You also already knew in your gut that he isn't taking you seriously. Don't waste your time trying to fix this, just move on.

Trying to control a man, is ne4ver a good idea. He is done with you, so just move on.

He's the one who disrespected you, and you apologized? Don't ever do that. Dump him, and leave him to jack off to internet girls who wouldn't glance at him once. He's a loser, and there's nothing you can do about it. Move on and find yourself a real man.

Your relationship is over. Tell him you're calling it quits if he can't even respond to you like an adult, then move on with your life.

If you cannot control your tantrums (most children over 8/9 can) maybe you are not ready for a relationship.

I think that him liking pictures of girls on social media only becomes a problem when he pays more attention to them than he does to you. In other words, if it is getting to the stage where his liking of these pictures means that he is neglecting your relationship then it is a problem. Furthermore, you also have a right to be angry if he is reaching out and flirting with these women via social media. 

With regard to him ignoring you, I would say that he probably needs a little space. My advice would be not to message him. He knows that you exist and will reach out to you when he is ready. If he is giving you the silent treatment then he wants you to feel guilty and message him so you would be playing into his hands anyway. After a few days, reach out and offer to work things out with him. I always believe that every relationship is salvageable. However, I think the first thing you need to do is to be proactive in making things work between you. By that I mean you both need to work on resolving the complications that caused this argument in the first place. In order to do that you will both need to think of solutions and ultimately, you will both need to compromise on certain things. If you are both capable of doing these things then you can make things work.