Can you get a wart under your toe?

Yes - plantar wart: Warts can appear almost anywhere on the skin. There are many different types actually. What you describe sounds like a plantar wart - that you may have acquired walking barefoot in public baths/swimming pools/shower areas? Warts can easily be treated though and there are a number of over-the-counter remedies that can be tried. A doc with liquid nitrogen or a dermatologist can help too.

Yes: Plantar warts come on the soles of the feet.