Next Steps After Auto Accident Hit And Run— Injury? [pa]

State is PA (Philly). Yesterday I was driving along the Main Street in the city when a car in the right lane beside me tried to swerve around a city bus, and crashed into the back passenger side of my (brand new) car. We both pulled over; when I exited the car, he jumped back in his and peeled off.

I was able to get the plate, make, and model. The 911 dispatcher advised me to drive to the nearest station and open a report, which I did. They recommended for me to stay aware the next day as that’s when any injuries might be more apparent— sure enough, I woke up with pain along my back.

What should my next steps be? Do I file a claim with my car insurance, or find a lawyer? I got a call today from someone claiming to be from the city offering to set me up with a visit to a health office and a meeting with their lawyer; they were also able to give me the name of the other driver, but didn’t have his insurance. I’ve never been in a situation like this, so I’d appreciate any advice.