I don't know if warts on dogs are the same as warts on people but I've had an occasional wart in my life time. As a kid and once as a adult, a small one developed under by eye.
My son had one on the top of his index finger when he was 14 yrs old. It got kind of big and a dermatologist removed it. It grew back bigger and he removed a second time. It grew back BIGGER. By then I was terrified of removing it a third time. It didn't seem to bother our son so we let it go hoping it would go away on it's own. It kept Growing, Growing, Growing, until it covered his top of his finger between his knuckle and first finger joint. One day our son finally noticed the wart and wanted it removed.
We took him to a new dermatologist who said, this is the biggest wart I've ever seen and proceeded to take pictures.
He was amazed and intrigued by this huge wart. He, also, said I can get rid of this wart within a week. I don't remember what he applied. I believe it was some type of chemotherapy medication and like Magic! that wart went away in about a week, leaving normal clear skin and never came back.
So, when I got that tiny wart on my face, under my eye and it started growing I was TERRIFIED!!!!
and began applying tiny drops wart remover on it. It went away and never came back.