Ok, if the driver wasn't backing up, then it wasn't his fault....so that's something.
But who pays for your medical treatment depends on how the no-fault laws of your state are designed. In my state (PA), if an injured passenger has his own car insurance, then that is who pays for his medical payments, regardless of fault. It may or may not be like that in your state. So contact your insurance company (if you have auto insurance) and ask them if they are supposed to cover you in this situation. Next in line (I think) would be the insurance for the driver of the car you were in, but he didn't have any so that's out. After that comes the at-fault party's auto insurance. And if they don't have auto insurance either, then your health insurance (if you have any) would cover it. BUT, your auto insurance company should be able to tell you who's responsible for your medical bills, even if they're not.
You can also file a pain and suffering claim with the at-fault party's insurance, but since this accident has a your-word-against-his aspect to it, they might give you a fight about accepting fault, especially because your friend doesn't have an insurance company to advocate for him. Worth a shot though.