Supplements can't replace the thyroid hormone that your thyroid can no longer produce. if you don't want to take prescribed medication you could try Thyrogold or Metavive, but they are more expensive than NDT from Thailand. It's your free T3 that you really want to raise as T3 is the active hormone (T4 is just a storage hormone and needs to be converted to T3). Getting B12, folate, ferritin and vitamin D into optimum ranges will help conversion. If you have high antibodies, selenium can help. Don't think glutamine affects it,; many people take it for IBS.
If you can post your latest blood test results WITH RANGES, someone can advise.
If your free T3 is high in range, and TSH is high it means your thyroid is struggling. You have Hashimotos if you antibodies are high. Gluten free and selenium might help stop antibody attacks. Your TSH drops as a result of your free t4 and free T3 going up, but when you start to go hypo, your free T3 stays quite high as your body tries to make enough active hormone to keep you going. Eventually it won't be able to do that any more. With Hashi's, you thyroid is gradually destroyed, so you will need to take medication eventually if you want to avoid heart disease and dementia. Some people believe that a ketogenic diet and probiotics for gut health will help.
You need RANGES (the numbers in brackets) for your results. 5,5 for free T3 is good in a range 3.1-6.8, but not a good in a range 4-7.3. TSH 3.5 is pretty high in a range 0.2-4.2, but not quite as bad in a range 0.4-5.5. Labs use different ranges depending on country and test machine used.
Folate should be half way through range and B12 over 500 to avoid permanent neurological damage. Ferritin is OK (over 70) Vitamin D needs to be at least in the high 90s. As you have high antibodies, you may be able to get a doctor to prescribe when your TSH goes over range or your free T4 under range instead of waiting until it TSH is so high.
You should improve with thyroxine, but many people need NDT, or T3 added to their thyroxine. You'll also need to supplement the low in range vitamins and selenium for the antibodies. I know nothing about calcium levels.
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