Oh gosh, I just tried this, only 2 drops of Lugol's 15% neat into my ear that has been itching me all day, and it burned like hell! The pain actually made me vomit!
I almost ended up in the hospital, the ambulance service advised me to flush with water for 20 minutes, which I did and it brought the burning pain down somewhat, but I was worried I'd caused real damage.
I can't believe they would inflict this on children. My advice, do not use Lugol's neat in the ear.
I used to get horrendous ear infections a few years ago. After 3, ineffective, courses of antibiotics and 4 months of near complete deafness, pain and tinnitus, I decided to use my Lugols 7%. that I had used orally a year or so previously.. I got an old eye dropper and cleaned it out with boiling water. I filled it 1/4 full of Lugol's and the rest with the boiled, cool water. I put 3 drops, into the ears 3 times a day for the next 4 days. The pain vanished completely, my hearing returned and the noises went away, never to return.
I got the idea to try this from reading a clinical trial conducted on children in the remore African bush, obviously far from the nearest doctor. They administered the Lugol's neat, and 10 drops a day, but I thought that sounded a bit harsh, so adapted down. They had complete resolution of ear infections, even supporating inner ear infections; they all went away - the trial must still be on the internet somewhere.
Hope this has been helpful. I know that if I ever get a painful ear again, I won't be going to the doctor, I'll sort it myself.