@fify-- I was on levothyroxine for a year. I didn't have any hair loss in the beginning either. But then, my thyroid started healing and producing hormone on its own. The levothyroxine dose started being too much and I basically went from hypothyroidism to hyperthyroidism. This is when I started getting hair loss, but it took me a while to figure out what was going on.
The hair loss was immense. If I just put my hand through my hair, I would lose 20-25 strands at a time. I wanted to cry after I got out of the shower and saw the amount of hair in the tub.
I had blood tests done and the doctor reduced my levothyroxine dose. The hair loss still didn't stop after that. I had another blood test the next month and since I was on the lowest dose possible (12.5ug, so a quarter tablet), I was taken off of levothyroxine completely. My hair loss stopped within a few weeks of stopping the medication. I started getting new hair growth at my temples after a month.