Can I get out of paying subrogation fees for an auto accident where intially no one was found to be at fault?

I was involved in a accident 4 months ago. I was making a right turn and she was making a left turn. I look in my mirror and she was coming towards me. We ran into each other. I had no insurance but went to court and paid a fine and received 4 points on my license. She said I hit her and I said she hit me? A week later her insurance claims department called, stated no fault was determined, pay for our own damages. About a month later a guy from the subrogation department says I owe for her damages. Never physically spoke to the guy. I called back after getting all paperwork together but he did not call back when I left a message. Now Wilber and Associates is having my license/registration suspended for not paying. The officer was not correct in blaming me for the accident. I have been trying to look up information if subrogation is legal in Missouri. I have see that this company practices illegal collection practices. What can I do in this situation?