why does this happen with my skin?

Two things.

You are obviously not exfoliating well enough. Don't over do it tho. Get a lufa and get off the dead skin. When you get out of the shower towel off aggressively. (don't injure yourself)

Then apply lotion.

Part of the problem - with itching - may be because it is cold out - skin dries in winter and when you take a hot shower it doens't help things.

Sounds like the lotion. Lotions are typically for your body, are you using a face specific moisturizer? If not, there's your problem. Exfoliating has nothing to do with it and it's not dead skin. Mushy balls = lotion. Flakes = dead skin.

You aren't scrubbing all the dead dry skin on in the shower. You are basically shedding so a new layer can be produced on your skin. Try one of those shower scrub things (I forgot the name). Get all the dead skin for a nice stop lotion rub.

Its not coming from your nails. Its dead skin. Make sure you are scrubbing hard enough to get the dead skin off. Try soaking in the tub for a while to loosen it up then scrub, scrub, scrub! And make sure you are showering or bathing at least every other day if not every day.

Its dead skin. It also comes from burns.... mayeb you have a cold or wind burn? Or sun burn? But it could just be dry pealing skin in general. What works for that is apply citrus fruit... like oranges. It takes off all the dead skin. Ir dry brush your face. Just take a natural bristled brush and use it for your face... look up body and face frushing. I hope that helped.

it happens when your skin is damp -- not super wet, but yah. It's dead skin. You can rub yourself down really rough with a towel after you shower and THEN put lotion on. :)

Exfoliate :D