As the almighty TSH test is low, I am surprised your doctor isn't at all worried. I'm afraid I don't really know much about hyperthyroidism, but if you are feeling unwell it suggests something is not right. I doubt a TSH of 0.01 can be explained by menopause, even if feeling hot can be.
Your T4 and T3 are right near the top of the range (or possibly over? You haven't given reference ranges so it's difficult to tell).
Hopefully someone else will be along soon with some more specific information for you.
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