Yes it is safe to take Iodine as long as you take the companion minerals and vitamins along with it.
Selenium, magnesium, vitamin C and B + real salt, much salt in your case.
Have you checked your body temperature? Low temp = hypo T.
I have cleared a few bladders like yours with Borax, Iodine and magnesium citrate / malate. Most on kids, but my mother had a similar kidney story like yours for years; also doing cleanse after cleanse without getting any better. She was quite ill actually.
After she started taking salt and Iodine (she thought salt was poison for her kidney so it was not easy convincing her) she was well within a year or so. She chose to go low and slow as she feared her kidneys wouldnt take it, while I prefer high and hefty dosages, both works!