I'm sorry you are having to deal with this. I've never had hyperthyroidism or RAI, but I had thyroid surgery (a thyroid lobectomy and then a second surgery to finish removing my thyroid due to thyroid cancer).
Hyperthyroidism is treated with RAI, surgery, or sometimes anti-thyroid medication can help, I think doctors treat hyperthyroidism more aggressively than hypothyroidism because the symptoms of hyperthyroidism include an increased heart rate (tachycardia) and atrial fibrillation (where the heart beats irregularly) and both these symptoms can be quite dangerous.
Surgery and RAI either remove or destroy a significant portion of your thyroid gland, so whether you did the surgery or RAI, you might end up needing to take supplemental thyroid hormone if you don't produce enough. I hope your doctor discussed the potential side effects with you and the potential for needing to take thyroid hormone. (My thyroid was completely removed, and I now take a supplemental thyroid hormone - it is tricky getting to the right dose, and having "some" natural thyroid function remaining is probably easier to manage than no natural thyroid function.)
From what I can find, the RAI may not completely destroy thyroid function. Depending on the dosage of the RAI, you may not need to take supplemental thyroid hormone but some people do. Surgery has many risks (including damage to the laryngeal nerves that control your voice and damage to the parathyroid glands which could cause problems with calcium regulation) as well as risks associated with general anesthesia... the surgical risks are all very low, but they do occur in some people, which is probably why a lot of doctors prefer using RAI over surgery to treat hyperthyroidism.
As to whether you made the right choice -- it's too late to go back now and not worth stressing yourself over it, and I don't think there is a right or wrong choice in this case. Hopefully someone who has made a similar decision can help answer your question as well, but if it were me, I'd probably have chosen the RAI myself because surgery seems to be riskier. (I ended up having to stay in the hospital for a night after my second surgery because my parathyroid glands were not working properly, luckily I think they were just temporarily affected by the surgery and are working fine now).
I hope you feel better soon, and good luck with the RAI treatment.