car accident: should I sign the settlement before the injury is

I was told there are different parts, now I am required to sign the Salvage Ducoment (the car is totally lost), but I am still in medical treatment. should I go ahead to sign the document, since the insurance company will move the car from the body shop and needs this document.

another question, the Salvage Ducoment reports the loss is almost 2k more than the payment that will be paid to me as I was told via phone. Is this normal?

Thanks for all info.