I was diagnosed with fibromyalgia back in 2004. I eventually ended up finding out that I had late stage Lyme disease. Since then, I've met so many people who had fibromyalgia who have tested positive for Lyme. I believe that fibromyalgia in most cases is actually an infectious disease or diseases, if you include the coinfections.
That said, I've also started taking iodine because I really think it will help with the Lyme. So far in just a couple of weeks taking iodine has brought my body temperature up from 96 to 98.
I wonder if your taking the iodine might be causing a herxheimer reaction which may be Lyme die-off. I've noticed that my symptoms have flared also taking the iodine so I am going really slowly.