Can I still work it out with my gf despite hitting her in retaliation?

So a few days ago my girlfriend and I had a massive row. It started because she was going on at me for texting this girl (which I only did because she had an ex-boyfriend on snapchat) then she’s a bit ill that day so she’s really sort of irritable and she hits me on the head for a small thing like not doing a dish properly (I sat down with a sandwich and she hits me on the head saying don’t get any on my dress, which is on the back of the chair?)

She can’t accept that she was wrong too and I keep on saying it and she hits me in the face, just lashes out and hits me. Then she starts going on saying she hates my family, that my sisters are both slags (they’re not) that my Dad is a horrible bully, that I am a horrible c*** that my whole family are horrible c***s and I’m flinching away from her with my knee and arms up to stop her hitting me.

So eventually I’ve had enough and I hold her wrists to restrain her, and she’s screaming at me and repeatedly slapping me across the face so I snap and I punch her once in the face, then on the way down hit her again.

I feel absolutely horrified. She had a bit of a black eye and a busted lip and blood from her lip. She was crying her eyes out terrified. I feel utterly sick. I am not a violent person but I was pushed to my absolute limit. I should have just walked away but I didn’t. I keep having horrific images of this girl, who I love more than anything, crying her eyes out.