Body Shop said I still owe a auto repair which should already have been covered by insurance!?

I was in an accident and was not at fault. The other driver took care of the damages thorough their insurance. They told me to take it to their adjuster who had a total bill of $2900. The Body Shop fixed it. I never signed anything and never received a receipt with anything. Not even a repair estimate. Weird I know. Anyways, I picked up my car and they told me that everything was paid for and gave me my keys. I stated “that’s it” and they stated yes so I left. Anyways long story short, 4 months later I receive a call form the repair shop stating that I have an outstanding balance of $2900. I am like,”you told me everything was paid for and that I didn’t have to worry about anything”. They stated that the insurance never sent them a payment and I responsible. I told them that they are Geico’s adjuster so they have to deal with it. Now i am getting daily call on my balance. What can I do?
Didn’t sign anything not even what they were going to fix. The body shop is an auto dealership.

call up their insurance company and tell them whats up

Vintage Motors shop and customer cars (longer version)