Fortunately, contemporary dancers and gymnasts had this problem solved long ago! Dance paws, or foot thongs, are pads of fabric that sit under your foot, securely held on by elastic, to protect your tender skin from nasties.
Originally designed to be invisible, dance paws have developed to become an accessory. Brands like Footundeez offer foot thongs in prints or with rhinestones!
Dance Paws on eBay