How do I manage dead skin cells that peel off like a shedding skin only on my nose?

Whenever I apply makeup, it always smudges around my nose.

It feels like whenever I focus on exfoliating my nose, the dead skin cells just keep coming back like peeling skin.

If I apply it too oilily, my makeup smudges, so I don't know how to manage it.

For daily care, in the morning I just let the toner absorb and moisturize, and in the evening I wipe very lightly with a Cica pad and moisturize.

I exfoliate once or twice a week, but dead skin cells on my nose keep appearing now that the seasons are changing.

Please share how to exfoliate your nose and how to moisturize afterward.