Thank you for your consult at DoctorSpring.com.
The chances are that you might be allergic to the radioactive iodine judging from your reactions as a child. Relate this information to your doctor as he can perform a sensitivity test to confirm the allergy before going through with the test. If you are allergic, you should not do the uptake test or the thyroid scan. Both require radioactive iodine, but as an alternative radioactive technitium is also an option. I would recommend you perform sensitivity testing for radioactive technitium as well before use. This will be a sure way for you to know if you are sensitive or not.
As far as radioactive treatment for hyperthyroidism, there are other alternatives to radioactive iodine treatment if you are allergic. Other options include antithyroid therapy with methimazole or propothiouracil and surgical removal or thyroidectomy. Discuss with your local physician or endocrinologist the suggestions I have mentioned and consider if they are a good fit for you.
Hope this helps, Please ask if you have any follow up questions. Take care.