In need of advice (Car Accident)

What is the name of your state? Virginia

About 3 months ago, I was involved in a car accident, in which my wrist and forearm were slightly injured (to this day there is still some slight pain if I try to exercise on it). The other driver and their insurance company (Progressive) were clearly at fault and quickly accepted liability. The injury I had I thought wasn't too bad, but it did hurt when I tried to exercise so I saw a physical therapist for roughly a month and a half. The physical therapist office said that the liable party's insurance company would pay for it so I went ahead through with the therapy. I also got a referral from my own health insurance (MAMSI) for this physical therapy office just in case I needed it. When I got my final bill it was around $2700, far greater than I expected it to be and I saw have a couple hundred dollars in bills (for X-Rays) from a local hospital. The physical therapy's office says that since the other person is liable, their insurance will pay for this but I am now wondering if they will indeed pay the whole thing?? In the case they don't would I be able to apply the referral I received from my own health insurance (which was not applied to this cost) to have some of the costs paid for by my health insurance and the rest paid for by the liable party's auto insurance? In a worst case scenario, would an attorney be able to recover damages for a bill that high so that I won't have to end up paying out of my own pocket in the end. I'm meeting with Progressive's insurance adjuster tomorrow (to possibly reach a settlement) and I'm trying to figure out what I can do so that I won't have to pay part of a $3000 total bill... any advice is appreciated!!