The cause is irrelevant. Even if your AD's led to Iodine deficiency its likely not the sole cause and it likely just sped it along. I would wager there is not one human in the first world who gets optimal levels of all nutrients.
Iodine does not work alone, your symptoms could be caused by a myriad of things and instead of spending time looking for a smoking gun focus simply on providing your body ALL of what it needs.
Far too many people look at just this or that specific nutrient that they often cause more harm than good because they ignore others that are just as critical and in short supply as well.