I hope you had your police report.. since it's a rear end collision.. u dont have to worry about anything.. at all.. just get the medical treatment everything is gonna be paid by the insurance of the other party..  Also there is something called PIP (Personal Injury Protection) that makes all the medical payments despite of whose fault is it.. so dont worry at all for the medical treatments... 

And why do  you wanna sue?? is the other party not accepting it is their fault or what?? for me it seems pretty straight forward...