Not unless there is a lawsuit. During the claims process, the auto insurance company is entitled to investigate only the injuries you suffered from the car accident, or injuries you claim are worse because of the auto accident.
If you allow the opposing auto insurance company access to your records, read the form before signing. Cross out or rewrite any wording that grants access to your entire medical history.
If there is a lawsuit, you may have to turn over all your medical records related to the car injury or that could be related to the auto injury. For example, if you hurt your arm, you would probably have to give up old records about a broken arm, but not about a tonsillectomy. On unrelated matters, you are entitled to medical privacy. An experienced auto accident attorney can help.