Are foot warts supposed to be painful, or is there something else going on?

Maybe something else. Foot warts sometimes cause pain. The pain can also be due to some other problem. Foot warts can cause pain by growing into the foot. This is more likely to happen if the warts are on the bottom of the foot. The person stands and walks on the warts, so they can't grow outward from the skin like a hand wart does. Instead, plantar warts have to grow into the foot and push up on foot tendons or bones.
Warts . These can easily be painful . See your podiatrist for treatment .