Corporation Totaled My Car Test Driving It For Tpms

Location: BRONX NY

Manager called me few hours later after dropping my car off saying my car was totaled after being taken for a test drive by a worker. I get it stuff happens, pissed off but both individuals in the vehicle were ok and neglected medical. How ever, it gets sketchy because first I get a unknown call from an officer, she tells me 2 different names then I state mines and she asks why i said I wasn't the owner, i was confused because it was my first time speaking with her, fast forward she gives me all the information and I note everything down and record our phone calls. Then I go to the place where my car was supposedly towed then it ended up being at a different spot. Got to the 2nd spot where it was saw, the damage and spoke to the tow driver and told him about it how Pepboys totaled my vehicle. He was surprised because he thought I was the one driving and how in the camera footage one person flees the scene and someone else comes to sit in the car. Tow driver shows me the names they gave and they gave mines even got my last name wrong. On top of that when I went to the house of where it happened the person who opened told me how one of the individuals fled the scene after the crash and someone else came. They also had my vehicle on the tow truck even before calling the cops, and the only reason cops were called was because their neighbors had called. In the end I feel like there was something else that would have happened if police did not arrive to make a police report because firstly they were impersonating me , making the officer ask me why did I say I wasn't the owner when I stated my name to her over the phone, on top of that the tow driver first thought I was in the vehicle when it happened because they gave them my name to them and he told me how the people driving switched and one of them fled and someone else arrived to the scene. I was told to sue but am not sure if I should just go thru insurance first and if am not satisfied with what they offer, take it a step forward.

The corporation is Pepboys and my car was a 2018 BMW M3 with only 18k miles, I am in the military so i need a mode a transportation to go back to my base because I came back home for vacation days to see my wife and son. I spoke to 1 Firm so far but they said they would reach out back to me as soon as they gave my information to an attorney of theirs. I just want to know what can I do or should for now since I think I can sue for property damage, loss of use, emotional distress, and punitive damage. Should I even interact with pep boys before I speak to someone or just let insurance handle it? however I do hear their insurance is very difficult to work with and I only have half a month left here. Thanks and hope to get responses.

EDIT: Thank you very much to everyone that has commented and given me advice, I really appreciate it and am a 19 year old Marine which explains the grammar