[AbiDrew85]

Actually that doctor has oversimplified a much more complex situation.

Check these out:
http://www.stopthethyroidmadness.com/iodine12345/
http://perfecthealthdiet.com/2011/05/iodine-and-hashimotos-thyroiditis-part-i/
http://perfecthealthdiet.com/category/nutrients/iodine-and-selenium/

So, I'd suggest getting your iodine tested, as suggested by the first link, though I rather suspect you're low.

IF I'm right, then take:
http://www.swansonvitamins.com/swanson-ultra-concentrace-ionic-trace-mineral-drops-8-fl-oz-236-ml-liquid
http://www.swansonvitamins.com/world-organic-liquid-potassium-iodide-2-fl-oz-liquid

I'd also suggest still taking a thyroid glandular. I take the concentrace btw, but don't supplement my iodine, my levels are seemingly fine.

A teaspoon of concentrace and 2 drops of potassium iodide. Absolutely no more than 4 drops of iodide and a teaspoon of concentrace.

You might also want to supplement Vitamin C, but the way I understand your diet, you should be getting plenty of that.