Ever since I was a kid my palms and soles were dry and at the contact of water for about 5 mins it would leave them white as though they had absorbed water. And when it absorbs water the peeling of my skin on the palms and soles are easier.
Throughout my life there are, what I call, "Peeling seasons" where my hands (palms) and upper half of my fingers start peeling or more than usual. And these are dry peels not moist peels. When I peel the skin off my palms and fingers, the lower layer looks nice, somewhat moist and smooth. And then, after a few days it goes back to the regular dry palms and dry upper-half-of-fingers.
When I rub my hands (palms) on my arm it almost feels like sandpaper. And the skin on my palms look kind of thick even though it isn't.
I have tried lotion and moisturizer and it only gives temporary moistness, but most lotions make the peeling worse while providing moisture.
Whenever I wash my hands with soap it smells like soap, but throughout the day after about 3-5 hours my hands stink with a pretty sour smell. My hands were dry throughout the day so I doubt it's because of sweaty hands.
My soles and toes are a bit different. They don't really have any "peeling season", but rather peel regularly (not a lot). The dry skin that gets peeled off are pretty thick (maybe about 1-2 mm)
My feet doesn't stink as much as my hands though, which is kind of weird. And the peeling regions usually look kind of red/pink whereas for other people (normal skin) it takes on their normal colour.
Not sure if this helps, but my nails are all looking normal (not white or receding) with the exception of my left thumb nail having a vertical dark line that doesn't disappear.
To add more, it doesn't spread to other parts of the body or to other people.
Sorry for the long post. Thanks!