Minor car accident: no police report, don't know who fault?

-That is small and old street. I drove on the far right and ready to turn right. I drove slowly. But there is an other truck on the left lane behind my car. They went a little faster than me and then my mirror (on the driver side) scratch her truck a little bit on her passenger door side. I thought it was her fault but she claim that is my fault because I go over her lane a little bit. I also thought she went onto my lane but actually I don't know. It just happen so quick and I couldn't tell who is responsible for the fault. There are no police report and witness.

Then she and I report to my insurance company. I claimed it is her fault, he claimed that is my fault. The insurance company don't know what to do because both said the same thing. They are waiting for her insurance company to decide. Then if it remain same situation, they may turn the case to the court.

This is my first time involved in the car accident, I know it is very small, minor accident, no one hurt. What should I do? should I said it is my fault? (even I don't know) because I don't want any problem ruining my life. If I say it is my fault, there are any effect to my insurance? I actually know nothing about this. Please help me!