The insurance company has asked me to sign paperwork that gives them access to my medical records so that they can make me a settlement offer. Do I have to do this?

No. This is a common request by the insurance company, and it is overly broad.  You do not have to allow them to get every medical record you’ve ever had before you can discuss settlement with them.  If you have any questions about what is relevant and what isn’t, you should consult with an attorney.