White on the soles of the feet

It looks like a white, hard, and firm spot on the sole of the child's foot, but I'm not sure if it's a callus or a wart.

It is the convex sole area below the big toe.

They didn't say it hurt even when pressed.

I bought some medication thinking it was a corn, but it doesn't seem to go away easily.

The problem with the walking gait is so severe that even the shoe sole has a hole worn through that part.

Should I go to the dermatologist?

Please recommend.