When you have an iodine deficiency, taking a maintenance dose can make changes slow. Better to take higher amounts of iodine for a while.
I have no idea what might be available there for iodine supplements. 500mcg - 0.5mg iodine is often available in a kelp capsule. If you have shops that specialize in vitamins etc, talk to them. There might be iodine liquids in dropper bottles which can be used. You put in water and drink it, might be a bad taste. Also see if there are other options for selenium or multi-vits with more selenium.
Fluorides can interfere with iodine, but the bigger problem is bromines. High dose iodine does flush these out of the body, but this is a rare need or occurrence.
Back to the main event.
I have no idea what is making your FSH so low.
Your labs do not help very much because there are contradictory signals in the data. Would be good to repeat: TT, FT, LH, FSH
Over training can cause problems.
Have you read the things that can damage your hormones sticky?
Your written English is very good!