Hit and run

Someone side swiped my car. We were turning left and merged onto me and swiped the driver's side of my car. We both parked on the side and the person came out to ask for my license and insurance. I asked them for theirs and they said they were not insured. I said i will only show them mine if they present me with theirs. As i was taking photos of the damage on my car, this person suddenly drove off. Luckily, i got a picture of their plate.

I filed a police report and a claim to my car insurance. Sent all documentation that the accident was on the driver side middle part of my car (door). I have a friend who owns a shop who gave me a good rate so I paid out of pocket. My insurance said 0% liability. I thought it was done but still kept my documents.

Then, i received a call saying that the person who hit me is filing a claim saying it was my fault and since both of us says differently, it will go to arbitration (so apparently they had insurance all along and didn't share the info). I called my insurance regarding this and they said i had nothing to worry about since I did the right steps.

I guess the concern is, is there a probability that I have to pay to repair the other person's damages? This is in los angeles. I just want to end this problem and get on with my life and not stress about possible additional expenses.

Thanks.