Ask the doctor to do a blood test to check your immune system and for any other abnormalities.
I know it sounds daft, but last week on UK TV Embarrassing Bodies, there was a person with the exact same thing. Trouble is I cannot remember what they called the condition she had, but it was an immune disorder.
Another person had Lupus and his feet were bad.
In the meantime, all you can do is to soak your feet in warm water with baby oil, use a pumice stone to gently rub away some of the hard skin and apply lots of moisturiser cream. You may benefit by buying cotton socks so that when you apply the moisturiser cream on at bed time you can put the socks on to keep the cream on your skin on not on the bed sheets.
Best wishes.