Help please.

I have suffered from white patches on my feet for the last ten years.
Basically whenever my feet get wet, be it in the bath or when wearing shoes - sweating a brilliant white patch appears.
The skin on my feet seems to grow so fast and hard in these areas also.
I have been to a podiatrist no joy, ive tried to treat it with athletes foot products and still nothing. The only time it doesnt happen is when I dont allow my feet to get wet ie- have a bath with feet hanging outside of bath (not much fun as you can imagine) and then the skin is very hard and thick.
Im not sure if is something internal as it happens on both feet.
Winter is upon us again and am dreading it as my feet have no choice but to be covered allday. i cant go swmming either.
I am at my wits end will try anything. appreciate any advice
Cheers!!