Thanks,everybody.Geico said something 3rd is at fault but

My conern is my medical expenses. I didn't pay for medical coverage with Geico so I can't use it and will have to ask the the third car's insurance to cover it. I hate to haggle with them. I hope I can use my own health insurance from my employer but I put down auto relAted already so I'm afraid they may ask me to pay for it. Shouldn't be too honest. I did call them today. They said I can call another company they r contracted with and they will ask the third cars insurance to pay for it. What if they can't get it? Will I be responsible for it?