Violent love

My boyfriend and I have been together for a few years now. He is 17 years older than me... I am 26, we love each other no doubt . We are in a long distance relationship and I recently visited him in New Orleans. We had a great time until we both drank too much, we got into a huge fight and I said some every offensive things to him. They were so offensive that our argument got physical and in the end he dumped me. 
Now I'm bruised and single and heart broken  and I want him back so badly. I know it's sounds like a typical situation for a lot of women. Now I look like the woman who gets hurts by her boyfriend and constantly runs back to him. Although he has made it very clear that he still loves me but will NOT get back together with me due to the harsh words I said, and the violence between us.
Am I completely blinded by love? Am I crazy for wanting him back, he's been my life for years now and I don't know how to focus on myself anymore. 
Any advice?