I doubt magnesium oil would be enough, although it has its uses. We generally recommend oral magnesium citrate or magnesium malate. You need a minimum of 400 mg of the magnesium component, up to around 1200 mg according to your bowel tolerance before you get diarrhea.
I think chlorine is nasty to the body. I gasp for air around chlorinated swimming pools, and my husband got bronchitis the last time he took a swim in one. I think you could be right, that this is the source of your trouble with iodine.