Who's Insurance?

Hello! So I was a passenger in a car accident a little while ago. We got rear ended on the highway and the other driver took total fault for hitting us.

So I had some whiplash, concussion, etc stuff to deal with medically after the crash. My physical therapist said they couldn't work with me unless I took out a claim with my own insurance no matter what the circumstances were. Now my insurance (progressive) says they don't want to pay and the want the driver of the car I was in to pay, but again, the driver that hit us claimed total fault.

Has anyone dealt with this? I guess just medical/auto insurance when you're a passenger in a car (not on the policy at all, not my car, just a passenger), where the other driver has claimed total fault?

Thanks!