Good Day, My Thyroid Gland Was Overactive After The Birth

Good day, My thyroid gland was overactive after the birth of my first child, I had thyroid treatment for 3 years but it stay over active, my thyroid was partly removed, but was still over active, i had chemotherapy to destroy the other half, now my thyroid is under active, i drink Eltroxin 0.1mg twice a day, i feel good but i have a problem with my hands that shake a lot, which is very embarrassing, i am a smoker can that be the problem for my hand that shake like that?