Normal range for TSH is 0.3 to 3.0. AT 0.01, it would apear you are overmedicating, and are currently more Hyperthyroidic.
Now, I'm not as knowledgeable as others here, and by all means, you and your Doctor should decide what to do.
But I think most people would be pretty hyper with a TSH like that. I know I would be bouncing off the walls. Could it be that some of your symptoms are somewhat anxiety induced, because of being currently in the Hyperthyroid range.
Your decision to reduce your dosage, might well be what your Doctor will agree with.
My opinions only, not medical advice. Always follow advice of your Doctor, not what I say here.