u/Comfortable-Fun123

I was in a car accident yesterday where I was stopped in traffic on the freeway and someone rear ended us at full speed like 50-60mph. My partner and I were in the car and both of us feel badly injured we got checked out at an urgent care and they think we have bad whiplash. My car seems to be totaled although I have yet to get it evaluated. I filed a claim through my insurance (Allstate) and the adjuster contacted me telling me the other persons insurance (State Farm) is willing to take 100% liability. If I file with mine I will have to pay deductible and have my rates possibly go up but if I file with theirs I worry I will be going through the process my own. Any advice on what route I should take?