I too would be very happy if i could get those results on T4 monotherapy and your doctor is reciting the usual dogma regarding the TSH and not looking or understanding that if your T3 and T4 are in in range then everything is fine.
I'm guessing your high inflammation is due to Hashimoto's as that can compromise T4 to T3 conversion, and presume you have read of Dr Izabella Wentz's research and work on how to reduce these auto immune attacks through abstaining from certain foods and repairing one's gut.
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