adenure
Hi,
Welcome 
I was diagnosed with Graves after my 4th baby was born. I felt fine the first 2 months of his life, and then things went bad pretty quickly! My endo did antibody bloodwork and a radioactive uptake scan to confirm that it was Graves (instead of postpartum thyroiditis). If you’re breastfeeding, and you do the uptake scan, you will have to wean temporarily (the number of days depends on the radioactive material used for the scan).
I would suggest trying ATD’s (anti-thyroid drugs) like methimazole or PTU to start as you’ll be able to continue breastfeeding (if you are nursing) on those medications as long as they don’t exceed 20 mg. daily (methimazole) or I believe 250 mg PTU (not sure on that one though). Plus, you will hopefully get your numbers leveled out (thyroid levels) and you will have time to think about whether you want to continue on ATD’s, choose RAI or surgery. If you choose RAI, you would have to wean your baby completely and not be able to nurse again. But, if you’re not nursing, that’s not too much of a concern.
It’s good to have a choice in treatments because no one treatment or medicine is right for everyone. I would ask for antibody testing though (blood work) to have a more certain diagnosis of Graves vs. postpartum. The uptake scan is the only 100% guarantee for diagnosis, but antibody testing is 95% accurate as my endo told me.