Hello again and thank you for your reply and the additional information. It is likely, but not certain, that you would not have an independent cause of action against the doctor for medical malpractice that you could sue for. The reason is an legal doctrine decided by the Supreme Court decades ago. It is called the Feres Doctrine
and that essentially states that a servicemember may not sue the Government, and in most cases an agent acting on behalf of the Government, for a negligent act that occurred incident to their military service. As a result of this doctrine, the Federal Torts Claim Act was enacted.
Under the FTCA, a servicemember can file a claim for a negligent act and it is processed much like a workers' compensation or insurance claim is. It is fairly complicated to explain and ultimately you will need to sit down with a local attorney who has experience with FTCA to see if, not only would it apply in your case because of this civilian doctor paid by TRICARE, but also because of the time line. There is a 2 year statute of limitations from the negligent act. There are some circumstances though, that are usually litigated, where the 2 year period might start when the negligence could have been discovered for the first time. So, this is by no means straightforward either way in your case.
I am fairly certain that the courts in your jurisdiction would find that this procedure falls under the Feres Doctrine and therefore, the FTCA would be your only option. If, by some odd chance, they would find that Feres did not apply here, then if this procedure was done in Mississippi you would have a 3 year statute of limitations. Again though, the statute can be extended in certain circumstances and you must speak to a local personal injury (trial/litigation) attorney about this.
Finally, just so you know. If you do have an ongoing disability or medical issue from this, you will likely qualify for VA Disability Compensation and should apply for that as soon as you can after you are discharged. Of course, you can also receive medical care through the VA.
Please let me know if you need any clarification. I would be glad to assist you further if I can.