You can sue your doctor for anything. The real questions are whether or not you can get to the jury under the Alabama Medical Liability Act and whether it is economical to bring such a lawsuit. Under the medical liability act, you will need a similarly situated physician to testify that your doctor breached the standard of care in his/her treatment of you, and as a result of the breach of the standard of care, you were injured and damaged. These experts are expensive.
Given your explanation of what occurred, it is very unlikely that you can locate an attorney to handle such a case. This does not mean you do not have a case or that your claims do not have merit, but these cases are so difficult to win in Alabama, and they are so expensive to pursue that it's hard to prosecute them with any expectation of victory. Consequently, the payoff must be substantial in light of the risk.
For example, would you be willing to invest approximately $100,000 of your own money into your case for a potential $200,000 or $300,000 verdict in two years and a risk of a $0 verdict? That would be what you would be asking an attorney to do. Usually, these types of cases involve amputation, paralysis, or death, and the potential verdicts are in the seven figure range.
I hope this helps answer your question.
To add to the answer that you have already received, you did not mention whether the treatment for Graves was successful at resolving your anxiety. Also, it is not clear whether your Graves existed for that long. These are questions that you will be confronted with in a lawsuit. There are many others also because you will bear the burden of proving the doctor was negligent and that caused you harm. As a practical matter, it seems unlikely that you could pursue a medical malpractice claim here in such a way that you would be left with any meaningful amount of money in the end due simply to the extremely high cost of pursuing such a case. As always, this is just my opinion and you should seek additional legal opinions before you make a final decision. There are time deadlines involved so I encourage you to seek another opinion as soon as possible. Good luck to you and your family.