Fender bender in intersection

What is the name of your state? NY
We are at a stop. I am the 2nd vehicle.
Light turns green, we both go, I hit the other car (SUV).
I haev a lot of "sheet " damage as the tow guy says.
radiator was toast.
The other guys bumper was hit.

That was it. the guy seemed fine. On the report though they police listed injured , 1 person.

Should I get a lawyer? I have not been contacted by the other guy, should I contact first with a lawyer, or let the insurance deal with everything.
Sorry this is my first accident. I am so afraid.

You submitted a claim to your insurance company, correct? Let them work it out and see what happens before you get worked up about nothing.

ok I will wait for them, yes I sent a claim.
thank you!