Vitamin E is generally not high enough in multivitamins. 400-800 IU recommended when recovering from a thyroid issue.
Vitamin A doesn't get enough publicity either. "Thyroid hormone plays a role in the conversion of beta-carotene to vitamin A. " If you've had low thyroid for a period of time, you might be deficient in Vit A despite supplementing with beta carotene. If the palms of your hands and the bottoms of your feet are orange, then you might not be processing beta carotene properly. Check your multivitamin and consider adding straight vitamin A. http://www.naturalendocrinesolutions.com/articles/vitamin-a-thyroid-health/
And lastly, don't drink tea. I've already written pretty extensively about my experience with tea, so I won't explain more here, but if you want to read about it, you can search for tea and fluoride and you'll find more info.