I was recently involved in a pretty serious car accident and I'm wondering if I should hire a lawyer.

I was rear-ended by a driver whose plates had been cancelled, and from what I've been told they may not have had valid insurance either. My car is a 2019 Lexus ES350 and there's a chance it may be totaled. I went to the ER afterward because of shoulder pain and I'm still having some discomfort.
I have my own insurance and have already started a claim, but I'm unsure whether it's worth hiring a personal injury attorney or if I should just let my insurance company handle everything.
For those who've been in a similar situation:
Did you hire a lawyer?
Was it worth it?
If the other driver had cancelled plates or no insurance, did a lawyer help you recover more money?
Are there any downsides to getting an attorney involved early?
I'm located in Connecticut if that makes a difference. Any advice or experiences would be appreciated.