Can I do genioplasty or jaw surgery with thyroid issues, if so which should I have? (Photo)

It depends what you are looking for/need. Without having any background information, it is hard to say. The xray shows and underbite, which may entail having jaw surgery. Jaw surgery is a major procedure that is done to fix breathing issues, sleep apnea and bite. If you are having these issues then I would say you should say to have them fixed for better overall quality of life. If you are just looking for aesthetic reasons, a chin reduction is possible, but there is a limit on to how much can be reduced. As for the thyroid issues, it would depend on what they were and medications you are taking. If the issues are well controlled and the surgeon is aware of it, then both surgeries should be available to you.