...insurance company? The other guy ran the stop sign, and I broadsided him as a result. I hit both my knees on the bottom of the dash. My back is sprained. My mom was in the car too; she hit her knees against the dash also.

yes- for many reasons.

First off, you are contractually obligated to do so- they will find out from the police report anyways.

Second, they will be able to answer any questions you have about going through the other drivers insurance.

Third- in many states- regardless of fault- you own insurance is primary for injuries. If you both are really injured and are treating- you do want them to pay right?