How to treat dry, flaky skin around the mouth and nose during the change of seasons

White flakes of dead skin appear around my mouth and nose during the change of seasons. How can I get rid of this?
Lately, the areas that really stress me out are the sides of my nose and around my mouth. It’s less of a problem elsewhere, but for some reason, only these spots get messy, white flakes of dead skin that completely cake my makeup whenever the seasons change. I’ve tried picking at them with my hands or doing some home care, but it just falls into a vicious cycle where the flakes get even whiter over time. It’s driving me crazy because it bothers me every time I look in the mirror. Does anyone have any personal tips or tricks for calming down these white flakes or providing emergency treatment without irritation? It would be a huge help if you could share detailed treatment methods during the basic skincare routine—specifically, how to remove them without damaging the skin and leave it feeling moisturized and smooth.