If your TSH level is .02, I would assume you are hyperthyroid. Why are you still on that high of Synthroid? I would make sure your TSH reads what you say it does and ask your Dr. this question.
You could be med. induced hyper which is not good. In other words, your TSH is too low and med. dose too high for you to feel your best.
Discuess this with you doctor.
Happy Holidays -
GL,
My information is from reading material gathered from reputable sources, my 20 years of personal experience and as a thyroid patient.