Should I release my medical records to another driver's insurance adjuster?

You should never release your medical records to another driver's insurance company. In order for them to get your medical records, they will present you with a written release. You are probably not experienced in reading the terms used in that release. That release gives away your rights of privacy to your medical records. When you're presented with such a release, you should definitely contact an attorney who is used to dealing with the insurance company, who is used to handling personal injury cases and who will respond to the request for a release of your records.