I have given my own kids Iodine for 4 years now, all companions need to be taken, adjusted for their weight (more than years)
All kid cases I have given iodine, selenium, magnesium, vit B, C and boron. Some have had zinc in addition to this.
Very few have had reactions to iodine, but I have seen anger tantrums in the youngest ones in a transient phase. It is a good sign of temperature :)
First of all quit all fluoride possible. Get some real salt and use butter and coconut oil only for your cooking. It helps getting the temperature up and the thyroid to work.