Your child's reports suggest that she has hypothyroidism. While iodine deficiency, especially under the circumstances described by you, is a distinct possibility, one cannot be certain that it is the definite underlying cause. We should exclude other causes, particularly auto-immune thyroiditis. The treatment is relatively simple & inexpensive. It involves oral intake of thyroxine, the dose of which needs to be titrated by your doctor by frequent testing of thyroid functions. The treatment is usually prolonged, at least for a few years but if taken under medical supervision, free of side-effects.