Tapazole and my Thyroid?

Hi, I have Hyperthyroid and my doctor put me on Methimazole 5mg 4 times a day. Since starting to take the meds on day number 2, I noticed my hair falling out. Not a little a lot, I called my doctor and he indicated that this will happen but once my Thyroid is adjusted, this will no longer be the case. He states it should take about 4 weeks. My concerns as a 31 year old female, has anyone ever gone bald from this? What if all my hair falls out? Can I take something else? I read that it could be a side effect of the meds? If that’s the case then it will not stop until I come off the meds. My doctor is not concerned with my concern of hair loss and says that it will be fine. What do I do. Please help.
Ms. E,
My doctor is suggesting the RAI treatment. How has it worked for you? Do you take Snthroid? Does that cause your hair to fall out. My dr. needs to reg. my thyroid before the RAI treatment. What are your thoughts