I did Iodine a full year before I found this forum. I had to find my own way of doing it, with a little help from some Iodine sites.
What route to choose; up to you. But, reading your symptoms; yes I would jump right up to 100 mg, or more.
Low thyroid, the docs tests doesnt work very well.
Just make sure you take the co facors like salt, magnesium, selenium etc.