Yes you can try iodine; but I would do all companions as you may need a lot; like 150-300 mg the first time, for some days. Especially magnesium (2-600 mg) and vit C (1-5 grams daily) Selenium so your thyroid dont get shocked of all the iodine.
I would add a lot of real salt (celtic, himalaya etc) as I have had no touch of uti after I started to salt myself 4-5 years ago, before iodine.
I would also add borax pharmaceutical grade; a pinch or two daily, in case it is fungal. (this helped my son and other kids with frequent urination / pain that was suspected to be an infection) It works fast.
One thing that helped my UTIs before salt and Iodine was essential oils; externally painted on the skin from hip to hip + at the urethral opening. Internally would probably help as well; the strenght is different from brand and production method so you will have to learn by doing, generally lavender/rosemary is safe straight, but some dilution may be needed.
Oregano oil is great diluted, same as with Thyme and tea tree.
You may have tried some of this; I believe the trick may be to do the whole set.