How can I get assault charges dropped if my boyfriend hit me and they charged me with assault?

My boyfriend and I got into an argument after a night of drinking and he hit me in the face with a closed fist and busted my lip and mouth. I called the police and they cited me with assault because "our stories didn't match". I found out that he told the cops I hit him with a baseball bat, even though he had no marks or bruises and the cops never took photos of him, but they did of me. They even let him leave the apartment intoxicated. How can I get these charges dropped? My ex doesn't want to go through with this anymore either. I would just like to note that I did not assault him and he lied to the police. The baseball bat did not come into play until after he hit me and I was going to attack him back but he was already waiting in the kitchen with another blunt object and at that point I decided to call the cops or one of us is going to be in serious trouble. The cops didn't believe me, even though my blood is on the bat, proving that I didn't touch it until after HE assaulted ME.