I was in a similar situation to you many years ago.
I grew a "large multinodular goitre" and was instructed to have surgery as this is the only "treatment" offered by the medical establishment.
Luckily for me, the doctor allowed me to opt for a partial thyroidectomy even though both lobes were enlarged, one moreso than the other and very unsightly. Luckily for me only half was removed and I still have the other half intact. I am so glad that I still have half a thyroid as I was able to treat it using iodine!!! I no longer have pain and my remaining thyroid tissue has shrunk.
I think if you commence using Iodine now, you will be able to shrink your goitre over time. It does take time and it is a slow process, but at the very least it will stop growing and you'll get the Iodine your body is starving for.
An enlarged goitre is because your thyroid is swelling to take up Iodine because you have a deficiency. Give it what it needs.