Thyroid issues can cause absorption problems, and to me it sounds like you are experiencing multiple nutritional deficiency symptoms: brain fog, anger issues, forgetfulness, muscle aches. All of those are actually low thyroid symptoms as well. Are you having heart palpitations?
Low thyroid causes a slow down in digestion and a reduction in stomach acid which leads to nutritional deficits, and that in turn leads to more problems, and it's a domino effect. (One example: inability to create enzymes needed for things like converting beta carotene to vitamin A.) So low thyroid people are usually deficient in many things, but the top ones are: B12, iron, copper, iodine, selenium, vitamin A and vitamin D.
You've said supplements haven't helped. And zinc has made you feel worse. It would be good to know what supplements you've tried and how much of each. Also, timing of supplements can make all the difference.
Too much zinc will interfere with copper absorption. You mentioned zinc makes you feel worse. Worse how? Stomach issues are common if you take it on an empty stomach. If you feel worse in other ways, or if you get a metallic taste in your mouth from zinc, it could be you have zinc excess. Zinc excess CAUSES copper deficiency. http://ajcp.ascpjournals.org/content/123/1/125.full.pdf
Don't take more than 30mg a day of zinc. 15mg should be enough and I wouldn't take more than that just to be safe. Also, take it at a different time from any copper or iron you take.
Coffee interferes with absorption of several minerals. You mentioned you drink coffee pretty often, and the tannins in coffee could be interfering with nutrient absorption, especially iron and copper. So you should consider cutting way back. And take any supplements an hour before or two hours after your coffee.
If you are low in copper, iron supplementation won't do much for your ferritin because you need copper to metabolize iron into hemoglobin.
Copper supplements should be taken separately from iron, zinc, and vitamin C.
B12 supplements need to be in methylcobalmin form and preferably sublingual. B12 is especially key if you have brain fogginess.
Take your vitamin A at a different time than vitamin D.
This sounds complicated, but a good schedule would be:
Morning: Coffee, Iodine, Vitamin D
Lunch: Copper, Vitamin A, B vitamin complex with Methylcobalmin
Dinner: Zinc, Selenium
Bedtime: Iron and Vitamin C on an empty stomach
One more that you don't hear people discuss much is choline, which is important for the liver. It is known to help with anxiety and depression. It was only discovered as an important nutrient in 1998, which just shows that there are probably more things in food that we haven't discovered yet. You can buy this as a supplement or get it from egg yolks and beef liver! Yum.