Wow, that sounds awful! I don't have that problem, but I can help recommend some shoes. The best shoe for biking is a shoe with a very, very stiff sole. Clipless pedals and shoes are a good option because they'll force you to have your foot in an ergonomic position while you ride. I would recommend going to an LBS with your bike and having them fit you with some shoes and pedals so that your foot is pushing on the pedal in the right spot. If you don't want to go clipless, then maybe look into some freeriding shoes or track shoes.

Good luck!