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I have gone through the attached images. These are nothing but plantar warts. Also, the pin point bleeders confirm that it's a wart. A corn shows a white underlying thick base when pared. You can also differentiate between a corn and wart by pressing it. A corn is more painful when pressed directly/ vertically while a wart is more painful when pinched or pressed laterally.
Now to treat the same, you may apply salicylic acid and lactic acid solution in colloidion base(duofilm). Dip your affected foot in warm water for five minutrs. Clean the area with pumice stone and then apply duofilm lotion.This has to be done twice in a day. Usually, this clears warts in a week or two. We also prescribe five percent fluorouracil cream twice daily for warts. If no response is seen, you may contact a dermatologist for paring with cryotherapy or cautery.
Hope this helped.