Get your regular doctor to do a thyroid test (TSH and free T3 and T4 levels). If you have a thyroid problem, you need thyroid medications. I actually had lunch with a PhD a few months ago who was talked into this iodine painting business, so I looked it up - the absorption of iodine through the skin is negligible (effectively zero). If you really have an iodine deficiency (check your multivitamin, as it might be in there), I suggest looking into a kelp supplement, as it is basically pure iodine. Side note: get your thyroid checked by a doctor before trying an iodine supplement, as some forms of thyroid disease can be aggravated by iodine.
Here's good summary of why this doesn't work:
https://thyroid.about.com/library/derry/bl2a.htm