Avoid magnesium oxide. That is pretty useless. I tried it out. I was taking magnesium chelate capsules but that is too effective for me lol (developed kidney failure on low dose - my kidneys are not up to scratch apparently no doubt due to insulin resistance). So I switched to my current magnesium citrate in tablet form and not every day. I take vitamin D3 capsules. Usually 3000 IU a day.
Have you been tested for magnesium and Vitamin D? If so, please post results. Also, what symptoms do you have, if any? What are your Free T4 and Free T3 levels and daily doses of Synthroid and Cytomel?