In theory, you should be able to settle the claims separately because the the driver and his insurance company are separate. However, you will be required to sign a release of claims against the driver, and every release of claims includes a release of claims against the driver's insurance company. So, you will need to have the company agree to amend the release so you can pursue your claims against the company.
You should see if your state has any medical privacy laws that could give you a right to sue for the violation. You should also contact your state ins dept and make a complaint. Check with a local atty.
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