We have numerous testimonials about goiter that will help you - See Goiter-Swollen Thyroid here in our testimonials file: http://tinyurl.com/iodine-testimonials
IMO, yes painting the throat every other day then apply an oil such as coconut oil or grapeseed oil over the Iodine can help get Iodine into the thyroid.
However the main reason for the goiter is a severe Iodine deficiency in your diet.
There might be some additional swelling as your thyroid grabs at all the iodine it can get in your bloodstream. Blood is filtered through the thyroid multiple times a day and the thyroid has top priority for any iodine found.