I also have Hashimoto's and had some of the other issues you listed. A few things that made all the difference:
- Apple Cider Vinegar (cold pressed, not pasteurized), a sips worth in every glass of water (great for stomach acid and more).
- Chicken bone broth. As a former vegan this was a tough one for me, but it had an immediate effect on my feeling of well-being. I recommend putting a chicken foot or two in your broth and letting it simmer for over 48 hours. You can store extra in ice cube trays in the freezer.
- Coconut oil helps with Candida and is overall a great anti-fungal. Very good for you.
- Iodine. I had similar symptoms until I felt so bad one day I raised to 50mg. Immediately felt better and haven't looked back. I don't recommend you do this, though, until you are sure you're selenium sufficient, are taking all your companion nutrients, and are feeling stable and strong. Start with the above and work on strengthening your gut before you go higher would be my recommendation, though I am a relative newbie to Iodine, so take my opinion for what it's worth.
I also had the sore throat and all the bromide detox symptoms at lower doses, as well as a swollen thyroid. I was SURE I was getting a goiter until people here assured me that wasn't the case. I had faith, persevered, and am glad I did. If your thyroid gets bigger it will pass and may well just be swelling to take in the Iodine it is starving for. Mine went down within a few weeks.