As ringworm is of a fungal nature, Iodine may need a helping hand. What you could do is to apply iodine, then on top of that a solution of borax, water, tea tree oil and lavender essential oil (therapeutic grade)
This way the borax will reduce the stinging effect of Iodine as well as the boron + the essential oils get access to the worm transdermally.
I found this mixture very useful when I dealt with fungal infection myself, as it cover all possibilities, bacterial, viral, fungal infection. (some of these kritters have ability to transform) You may mix all of it and apply 2-3 times a day.