Make sure you hyperthyroidism is not caused by hyperstimulation by pituitary gland, not caused by a or several hyperfunctioning nodule(s), such as Plummer's Disease, not caused by transient release of thyroxin due to thyroiditis (again, many causes for this including autoimmune), not caused by exogenouse or ectopic thyroid tissue secretion, etc., etc.
You need thyroid nuclear medicine scan including thyroid function and iodine uptake. What are those results?
If I-131 therapy this is the correct therapy for you, the exac dosage need to be calculated based on your thyroid iodine uptake. Based on your age and symptoms (do you have hear racing, sweating, etc?), the dosage can be adjusted. In general, the therapy is safe and effective. Unless they kill all the thyroid tissue, your body can adapt to probable mild hypothyroidism, should that happen, by producing more stimulating hormone from pituitary glad to drive the remaining thyroid tissue work harder. So you need a competent endocrinologist and radiologist.
Good luck! Let us know if you need more information.