Another option is to quit Iodine for a week or three, I did this the first year when I suspected the Iodine was the cause of problems. It turned out for me that Iodine wasnt the cause, just highlighted the health problems I had.
In your case when taking tyrosine suppresing medication for your leukemia, it is difficult to see or even advice what to do further. Maybe taking the medication one part of the day, then taking iodine, and even tyrosine; another part of the day. As many of your symptoms is hypo thyroid; and tyrosine is needed for the thyroid hormone to work.