I ask becuase im pretty much in the same boat as you, as somebody has just driven into the back of my fiesta yesterday, and similarly, have been to the hospital and confirmed to have whiplash.
Same as you with being insured with admiral, but i have been in touch with Evans Halshaw Assistance (only any cop if you bought your car from there) which I know i got free for one year when I purchased my car last May. Was told by the advisor that it was 100% their fault due to being a rear end shunt, and that there would be NO excess to pay, and costs of a hire car would be recovered from them, not only that but it definatley would not affect a no claims bonus. To top that, they also offered to liase with admiral and guarantee that it would be repaired quickly in a ford garage, as opposed to the Brooklands bodyshop that admiral are contracted to in my area.
So in all, if you did buy your car within a year, from evans halshaw, would DEFINATLEY give htis a go