what can an insurance company do?

i got in a wreck with this girl back in november and they are claiming that it was my fault, but i wasnt at fault she was out of her lane and distracted by her phone. the police did not come because it was a private property but their insurance is sending me mail saying i got to pay $4600. i dont know what to do since their was no police report i didn't know you could still claim it to your insurance, and so i didnt. i called my insurance and explained after recieving their mail and my insurance said they will not cover it since the insurance was not purchased within 14 days of the car registration, i explain that i didn't need insurance since i didn't use the car but they still wont work with me. my question is. if they take me to the court or anything will i have to pay that money even though it was not my fault and there were no police report or anything for them, or what? i honestly cant afford anything since i am a college student. what is the best thing to do?