Is it possible to fight a family violence charge and press charges on the other individual involved?

I was charged with family violence. We were both drinking on mothers day and i told i needed to leave to go pick up money from a friend of mine. She stated she wanted to go with one thing led to another she ended up throwing a beer bottle and damaging my windshield to my car. I get out and she begins to strike me and punch me and kick me i grab her leg and push her to the ground and told her to come down at the end of the night she pulls a knife and holds it to my throat and threatens to kill me. then police show up and we tell them each our side of the story. They ask if i wanted to press charges i said no then they said if I'm not pressing charges on her then I'm under arrest. Supposedly my story didn't collaborate even though my windshield is cracked and i had injuries to myself.