I had an overactive thyroid back in 1978 and was given I-131 to kill it. I have been on synthroid or levithroid ever since.
No problems with it at all. About ten years after this I put a company geiger counter to my throat and got no reaction at all.
Thyroid cancer in 2005. Complete thyroidectomy followed by I131. I take synthroid daily. Neck ultrasound every six months by my endocrinologist and synthroid dose adjusted if needed. No recurrence.
My biggest problem has been fighting insurance companies, and now Medicare to stay on branded synthroid instead of being forced to the generic.
I had that done in 1991 for Graves Disease. Unfortunately, I developed Thyroid Eye Disease about 10 years later, necessitating 7 eye surgeries to correct it. My doctor only wants me to take Synthroid because of inconsistent dosage in the generic form.