You both committed battery. Let that be known loud and clear. She threw the first punch "so to speak" and you retaliated. Neither of you were right and both of you could have faced criminal charges.

The relationship is over. The best you can do now is to go into some kind of therapy to figure out why it got to this point and how to never be there again. For yourself, not as a couple.
As a couple, your days of working things out together, are over.

Wish her well, in time maybe you can talk through what happened but for now, it's best if you stay away from one another.

She was just as violent as you were, and neither of you were a victim and neither of you were right.