Someone hit me, they side swiped me

They tried turning left into turning lane then hit me, they then instead of pulling over immediately or pulling infront of me and going left to go to store they darted across the state road 3 lanes then pulled over looked like they were trying to run before I caught up and he pulled over immediately he gave me everything his license etc his license was suspended and he left before the cops got there because they were suspended he was driving someone else’s car, Allstate is trying to say he was on the insurance when the cop said his license has been suspended since 2019 they pulled up after he left I got a police report done still, the claims agent said they need to contact the insured driver first for their story, I have GEICO should I contact GEICO later today and explain to them everything in case Allstate and the other driver tried to fuck me, the other driver admitted and gave me everything and I have pictures Allstate didn’t ask me for the pictures, I don’t want to file a claim with my insurance because I just made a glass claim the day before it happened in Florida but I don’t want my insurance to raise I’m not sure what to do