I was recently involved in auto crash in FL, my insurance GEICO, isn't really fighting for me..do I have any legal recourse if this turns out poorly?

I hit a driver who crossed into my lane, she had a flashing red lite. She was cited, police report states she was at fault, but because I hit her back quarter panel, her insurance is pushing back. Geico was unsuccessful in subrogation proceedings. I don't believe they are really fighting for me, as it seems pr tty cut and dry? Since there were no injuries, is there a lawyer out there who would represent me if next phase, arbitration doesn't end with good conclusion?