I have just gone through it all; and things look great. So happy that they caught it early. Two words of encouragement.
(1) My surgeon, in my pre-surgery meeting, told me of a recent study that found that in a sample population those with papillary thyroid cancer live longer than those without papillary thyroid. (Maybe due to being cured and checked.) That was a very good thing to hear your doctor say.
(2) I was looking through the NY Times Book of Knowledge (or something like that title... big book). In the medical section they had the rate of US deaths from various cancers. Big numbers for breast, lung and prostrate. Went all the way down to a few thousand for eye cancer and other real obscure cancers. Thyroid wasn't even on the list. Didn't even make the list!!
So even if there are errors in these things, you're still RELATIVELY well off. Let serenity reign. You'll need an even head and optimism to get through the hypo/LID/RAI period... which is a cure for what ails you. If it wasn't caught I'd be here today with a thyroid swelling up and choking off that tight neck area. Want cancer... of course not. But now that I'm cured... it's a beautiful day.
RedStar