If the carbimazole is causing side effects you could try PTU instead. Some people get on better with it. How about beta blockers too.
Don't rush to have the radio active iodine, its not really a therapy, its designed to kill off your thyroid and leave you hypothyroid... This is then dealt with by giving you replacement hormones. It sounds simple but there are numerous stories of people who wish they had fought harder to keep their thyroid gland.
Do you have Graves' disease? HAve the antibodies shown this? or is it maybe a flare up of hashimotos? Get your blood test results, post them on here ad ame absolutely certain that you know exactly what is wrong before agreeing to any meds or operations which cause irreversible changes.
You work better with all bits intact and taking them out or killing them off can be just an easy solution for the doctors but not the best solution for you.
I'm about 80% sure that thyroid cancer is not treated with radio active iodine.... Its treated by surgical removal of the thyroid.... So that would make it more likely that you problems are auto immune.
Keep asking questions on here, plenty of people have been through similar situations.