Is it worth to hire a lawyer in a three car collision (not at fault)?

Hello.

I got rear-ended by two cars recently. I was the first car. Vehicle 2 slammed into my car. My car and vehicle 2 are stopped at this point. Ten seconds later vehicle 3 slammed into vehicle 2 and slammed into my car as a chain reaction. I had my two kids in my car. Police confirmed that I was the victim and both drivers got citation for not maintaining a safe distance. I couldn't get any other information because my kids were getting transferred to the hospital. I had to leave the scene before my car got towed.

My kids are fine. They are just experiencing soft tissue injuries.

Police told me that the police report wouldn't be ready until sometime next week and they can't give me further information. I called my insurance company (Geico) to start a claim, but they said I need to have the other party's insurance information if I want to use their insurance. After going through so many Geico agents, I finally got a name for vehicle 2 and insurance company (SafeCo) identified from license plate number. However, SafeCo wouldn't help me out saying I need to have more information to start a claim. Geico tells me that I need the police report so that they can help me go after the other drivers and insurance.

I am extremely frustrated. I had to pay to get my car out of tow yard so that bills don't start stacking up. It appears that other drivers didn't seem to report to their insurance company to start a claim for my damages either.

Will hiring a lawyer be even helpful in this case? I just want my car to be repaired and medical bills taken care of plus extra for inconvenience. Should I wait for the police report and see if anyone would do anything first?

Thank you!