This is Dr. David
if the cyst is bothering you, you can have a thyroidectomy and then replace all of your thyroid hormone with pills
this will be much more stable thyroid hormones for you
with graves disease, your body is making antibodies against your thyroid gland causing it to be over active.
by removing the gland all together or using I-131 radioactive iodine to destroy the gland, there is no residual gland left to be overactive and then you can supplement with thyroid hormone to be much more stable with your thyroid hormone.