About 96% of goiters are caused by an iodine deficiency. If you medicate with iodine, ideally with the simple prescription-free "SSKI iodide," it should best be done under careful supervision because, if overused, iodine can lead to hypothyroidism. However, eating iodine-rich foods, such as dulse (a seaweed), is a more indirect and safe way to increase iodine and shrink goiters.
At the same time, it is important to remove blood vessel wall and lymphatic congestion that are behind the poor nutrient supply (including iodine) and waste removal from the neck area and thyroid gland. Trapped lymphatic waste, consisting of metabolic waste products and dead, turned-over cells, leads to nodule formation and general thickening of the tissues there. The healing of any thyroid condition requires an overhaul of the digestive system, including the removal of all bile stones from the bile ducts of the liver (see The Amazing Liver Cleanse, ener-chi.com; this book also explains the connection between the liver and thyroid problems), cleansing of the colon and changing one's diet/lifestyle according to body type requirements (see specifics in The Key to Health and Rejuvenation, ener-chi.com).
And yes, avoid all dairy foods (except unsalted butter) meat, and foods that contain soy (thousands of processed foods contain soy).