Have you had a thyroid ultrasound to make sure the nodules aren't suspicious or anything?
What tests were done to determine whether or not your thyroid was "normal"? If your doctor only ordered a standard TSH test, you really have no way of knowing because TSH is only an indicator of actual thyroid hormone levels. It should not be used as the lone determinant as to whether you have a thyroid problem. You need to have Free T4 and Free T3 tested, as well. Those are the actual thyroid hormones.
Since you have nodules, you should also be tested for Hashimoto's Thyroiditis, which is an autoimmune condition that usually, eventually leads to hypothyroidism (under active thyroid). If you have Hashimoto's, it's not recommended that iodine be used to supplement as it can make the autoimmune response worse.