Was Rear-ended

My back is burning.

Like it feels cramping and it burns.

They police didn't call for an ambulance because there were no physical injuries.

I guess now that the adrenaline is calming down, the middle of my back burns.

All locations for urgent cared covered under my insurance are closed until Monday.

My question is: Do I have to be seen for it right now? Can it wait until Monday?

I was told to call the other person's insurance company to report it was my car that was hit so I am assuming I have to report this at the same time. The damage isn't too bad but he hit me while sitting at a red light.