The TSH test is quite variable. If you read my paper, you will note that,
Although considered as a sensitive biochemical marker, the guidelines3 recognize that “TSH levels vary diurnally by up to approx. 50% of mean values and with more recent reports indicating up to 40% variation on specimens performed serially during the same time of day.” And TSH has a weak correlation with either FT4 or FT3, and a negligible correlation with hypothyroid symptoms, due to the many variables in the total thyroid process. Why is it used by most all doctors for both diagnosis and treatment? Because it is so expedient, and has been used for many decades, even though there is much current scientific information to the contrary, like the link I gave you.
You still have a number of hypothyroid symptoms. I suggest that you go to this link and copy the list of typical hypothyroid symptoms and mark those you have, and add any others you have, and give to the doctor, and ask for an increase in T3 dosage.
When the doctor disagrees, refer him to the study in this link and especially click on Fig. 1c, which shows the significant effect of FT3 level on the incidence of symptoms. FT4 is much less effective and trying to determine thyroid med dosage based on TSH is totally ineffective. That is why testing and adjusting FT3 is so important. Don't forget to point out that everyone can be different in the thyroid levels needed to feel well. The same levels don't work for everyone. The objective has to be to relieve hypothyroid symptoms.
If the doctor says he doesn't need to test FT3 because T4 always converts to T3 as needed tell him there are numerous studies showing that is not the case. There are many variables that affect conversion, including lack of a thyroid gland. He can read all about that in my paper:
In addition to getting adequate FT4 and FT3 levels, it is important to get Vitamin D to at least 50, B12 to the upper part of its range and ferritin should be at least 100. If not tested for those, you need to do so and then supplement as needed to optimize.
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