I don't mean to sound rude or judgemental as I understand your reasons for averting Iodine, but I need to ask you if you're aware that you NEED Iodine for your body to function properly? Here's some bits I pulled from Wikipedia articles:
"Iodine is an essential element for life and is the heaviest element commonly needed by living organisms. (Lanthanum and the other lanthanides, as well as tungsten, are used by a few microorganisms.) It is required for the synthesis of the growth-regulating thyroid hormones thyroxine and triiodothyronine (T4 and T3 respectively, named after their number of Iodine atoms). A deficiency of Iodine leads to decreased production of T3 and T4 and a concomitant enlargement of the thyroid tissue in an attempt to obtain more iodine, causing the disease known as simple goitre."
"The thyroid hormones act on nearly every cell in the body. They act to increase the basal metabolic rate, affect protein synthesis, help regulate long bone growth (synergy with growth hormone) and neural maturation, and increase the body's sensitivity to catecholamines (such as adrenaline) by permissiveness. The thyroid hormones are essential to proper development and differentiation of all cells of the human body. These hormones also regulate protein, fat, and carbohydrate metabolism, affecting how human cells use energetic compounds. They also stimulate vitamin metabolism."
I am certain you will get better if you get yourself a good multivitamin with a 100% daily requirement of Iodine in the form of potassium Iodide. Let me tell you what I realized recently, it's kind of a funny story. For the past 3 or so years I have been puzzled by my constant fatigue, I tried everything, and I always made sure I was taking all the essential nutrients for optimal body functioning, and then about a month ago I stumbled upon some info about Iodine online, and it elucidated the grave importance of this element and I was fascinated with how instrumental it was in regulating all the other physiological processes of the body, so I looked at the multivitamin brand I had been taking for the past years and lo and behold: zero Iodine content. I was blown away, and so I bought a new brand with the recommended daily requirement of Iodine and in a matter of weeks, I started feeling alive again. My appetite returned, and I've become a healthy weight again. I was 67.kg a month ago, now I am 72.kg, which is the healthy weight for my height.
Please give it a shot, I created this account to talk to you and help you, so please do this, buy a reputable multivitamin with the recommended daily intake of Iodine, and see what happens. You have my word you will get better.