fatigue, psoriasis, eczema, and anxiety are all possible side effects of intestinal pathogens. Iodine can be pretty effective at killing intestinal pathogens but in doing so can temporarily exacerbate issues as your body has to deal with the dead pathogens and all the toxins they emit.
Iodine shouldnt directly be the source of intestinal issues except in the case of stomach irritation due to high dose Lugol solution.
Intestial pathogen die off and the escess toxins it producses could also account for some weight gain. When the body is overwhelmed and unable to eliminate toxins it will often create and store toxins in adipose tissue.
While using Iodine its important to make sure you get ample selenium as well as the additionally recommended co-supplements. I like to emphasize vit C intake because its a powerful antihistamine and anti toxin. Ascobic acid or sodium ascorbate, as much as you can tolerate daily without diarrhea. In your case you could probably boost the vit C inatke a bit to help keep bowels mobile as well.