First off, welcome to xibase...
Secondly, if you both love each other enough to love although he may get on your nerves at times, then you might think about trying to work out your problems together. If it got to a point where you became so frustrated with him, that hints towards there being a bit of miscommunication (bop me on the head if I'm wrong
).
I'm no expert on that thing they call love, but if there's one thing I know about, it's miscommunication (I should know, there was plenty of it in the limited experience I've had at it)
Miscommunication -> Stress -> Frustration -> Anger -> Pain
If you really want to make the relationship work, try to find some common ground where you can start to reconcile your differences. Remain, above all, communicative, it is the one and only key to maintaining a relationship.
As to whether you want to remain broken up is up to you. Nobody but yourself can convince you otherwise.