I can understand your concerns. Let me assure you that it is a safe and effective option.
In a case of hyperthyroidism
which is not adequately controlled with medication the appropriate treatment is radio-iodine
I am a practicing nuclear medicine consultant. Radio-iodine is perfectly safe and effective treatment in hyperthyroidism. The dose that is prescribed for treatment of hyperthyroidism does not have any effect on reproductive function. But it is better to post-pone planning the pregnancy
for 6 months -1year incase you need a second dose of iodine.
You can go home after taking radio-iodine. Maintain distance of 1 meter and sleep separately for atleast 3 days so as to not give un-necessary radiation
to other members of family. After that you can be as usual. It does not effect your sexual life as well.
You may have mild neck pain
after giving the dose and this is only temporary.
There are good chances that your problem might be cured with a single dose. So do not worry and please go ahead with the treatment.