Along the lines of your sensitivity to iodine, I wonder if you're feeling the effect of breathing it in via the steam from the hot bath? That would give direct access to your brain.
2 mg a day for 9 months -- You're going to be detoxing for a very long time. There's nothing wrong with that, and it will probably keep your detox to a tolerable level -- except for the odd bath with iodine in the water. Between what you have stored in your body, and what you're exposed to everyday, your progress will be slow, depending on why you are taking iodine to begin with. Remember that even 2 mg a day will do your body good.
It'd be easy to say yes, but the truth is I don't know. I think you can follow your body's reactions to learn what's true for you, and what you want to do about it. You're already listening. :)