What Trapper said. Hashi's makes it essential to take selenomethionine.
A lot of people don't realize that thery're not just dealing with correcting a deficiency. Iodine supplementation needs to REPAIR damaged tissues such as in the thyroid and the breast. This can take time. The damaged tissues have sustained long-time oxidative damage and need to heal.
New receptors (sodium Iodide symporters) may need to be created. Your TSH may rise. Toxins must be displaced and sequestered out of the body.
As long as you understand what is happening to your body, that a master organ is being cleansed and rebuilt, cell by cell, you will understand why the thyroid may swell. You will understand the scarcity effect on a long-time damaged part of your body.