Can I fight a car accident case that wasn't my fault?

Question Details: Last year I was drinking with my sister and had to drive us home. On the way I was turning left on a green light but as I was turning there was another car which didn't stop when it was supposed to and it hit me. Out of fear, I decided to flee the scene because I had no insurance or license and I was under the influence. I was caught and arrested me but let me go the same night. A couple months later, they filed a subrogation claim on me but I wasn't at fault even though I was driving under the influence and did not have insurance or a license. Do I still have to pay money? They also filed a warrant for my arrest. What should I do and can I fight this?

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