You will be thrilled to know that I have personally discovered this new affliction, which is apparently generally reserved to children. But I am young at heart.
The dermatolgist did the primary treatment with a scalpel for scraping, followed by an application of liquid nitrogen. Now I have to put pads full of salicylic acid on the zone several times a week. However, I also discovered that the problem is not taken seriously by health insurance because the acid pads are not covered and must be paid out of pocket. I have additionally learned that sometimes treatment does not even work, but that the lifespan of a plantar wart is a maximum of two years.
I might be entering second childhood, because warts are supposed to be mostly a childhood affliction. And the box of pads says on it "for treatment of warts on children." I asked if there was an adult version and was told that there is not.
I had tried to post this info a few weeks ago but couldn't manage just with my phone while I was away. There is a plant called chélidoine in French, chelidonium in English, that gets rid of warts. Called herbe aux verrues in French. It works very well and grows everywhere at this time of year.