It is a common phenomena to feel very well for a period after coming off levo - or any thyroid hormone replacement, come to that. And to conclude that you never needed it in the first place! But the euphoria doesn't last. Your TSH goes up and your Free go down and you become very hypo again.
It's also a common mistake to think that all you need to do for a thyroid problem is to throw iodine at it, to make sure it has 'all it needs to make hormone'. But that isn't all it needs. It needs a lot of other stuff, too. And by taking too much iodine you are unbalancing things. You thyroid probably had all it needed, anyway, and the excess meant that it had too much. And that is really not a good thing.
What on earth do you mean by 'good for cholesterol'? What does cholesterol need? If you mean 'good for lowering cholesterol', then that is not good for your body. Your body needs cholesterol, it is an essential nutrient. Your brain is made up mainly of cholesterol. You need it to synthesise vit D and you need it to make hormones. It does not cause heart attacks or strokes. You are more likely to have a heart attack if you have low cholesterol, than if you have high.
So, if levo doesn't suit you, why don't you try NDT? Or T3 - with or without levo? You don't have to just sit and suffer. It's not a case of levo or nothing. And, also, there are other brands of levo to try, maybe you'll find one that does suit you.