As long as they didn't have safe auto or some bullshit substandard they should have 100k medical, minimum $50. Insurance company wouldn't settle outright for that though without some serious injury, but with a few legit medical bills they should have no issue shelling out up to $10k. Just keep going back for soft tissue treatment like chiro, massages, etc. and let the drs know it's related to an accident with potential recovery. They'll potentially charge more knowing they can throw a lien on their bills which will give you a larger recognizable bottom line on recovery and force the insurance company to play ball.
And as far as I know, unless you're in a seriously conservative state, you can't contract away to the ins co your right to recover pain and suffering, even if the insurance company pays all your bills and has sole rights to recover their payments. btw I'm an insurance defense lawyer... so take it either as true or a complete lie