E.L.
I also had Hyperthyroidism (Grave's Disease). I tried the medication for awhile, I took Propylthiouracil, but it didn't work and I had to have radioactive iodine. Now I have all kinds of problems with Hypothyroidism, and still see an Endocrinologist. I would much rather have been able to control it with medication. I also breastfed while I was on the medication, my doctor said it was fine. Make sure you ask your doctor all these questions, even get a second opinion if you want. It is serious, but very treatable.
Good luck with everything, I hope you start feeling better soon! :-)