Should I break up with him?

You guys need to get relationship therapy. Its very useful and will give you both the clarity to see what your relationship is and where its going.

1. Look at the reasons you guys are fighting. Try to see the pattern in the fights (eg. Is it something you're dissatisfied with him or vice versa? )
2. Take a minute and be honest with your feelings. How much do you feel for him? Why do you feel unhappy around him sometimes so much that you want to break up with him? How is he hurting you?

Now a few words of wisdom:
Infatuation says, We must get married right away! I can't risk losing you!

Love is quiet understanding and the mature acceptance of imperfection. It is real. It gives you strength and grows beyond you to bolster your beloved. You are warmed by his/her presence even when he/she is away. Miles do not separate you. You want him/her nearer, but near or far, you know he/she is yours and you can wait.

Infatuation might lead you to do things you will regret later, but love never will.

All the best :)
and feel free to msg me if needed.