Hair loss is part of hypothyroidism -- I am not convinced it's a side-effect of levothyroxine, but this may be the case. I would first increase the dose to get the TSH to the target range (around 1.0) then re-evaluate. The life cycle of the hair follicle is long, so often the cause of current hair loss is an event from 2-3 months earlier. Protecting the source of levothyroxine (ie brand consistency) is important, but with careful monitoring, you can change to another levothyroxine brand. T4/T3 combo treatment (ie adding cytomel 5-10mcg/day to the levothyroxine) has not been proven in medical research to help with hair, but some patients do report a benefit.
Take Care