Very thick skin with fissures on feet

Hello, I have very dry skin and, as a dermatologist told me, a lot more skinfolds than the average person (see pic of my hand). But On my feet my skin becomes very thick within short time, like 8-10 days after using a foot file it looks like this. When I had my appointment it wasn't nearly as bad as this so the dermatologist just said its dry skin.The skin can then be peeled of in parts which are about 1mm thick, which is where the red spots are from. My dad also used to have this condition. I just to have a foot fungus before, but between my toes. Can anyone tell me if this condition genetic or more likely some kind of fungus infection?