Is there an effective way to exfoliate during the changing seasons?

Perhaps because the weather has suddenly become dry lately, even though I cleanse my face thoroughly, white flakes of dead skin appear around my nose and chin every time I apply makeup—it's a total mess. No matter how thickly I apply moisturizer before bed, my skin texture feels rough the next morning, and I'm extremely worried. Using scrubs at home causes redness and is too irritating, so I am considering getting professional care at a dermatologist or aesthetic clinic. I am curious about the effectiveness of exfoliation care that gently dissolves old dead skin cells without irritation; would it really make a difference how well my makeup applies? My skin is on the sensitive side, so I am cautious because I worry that receiving improper exfoliation in this condition might further damage my skin barrier. I would really appreciate it if you could share your personal exfoliation tips or any treatments you found satisfying to see how you all maintain smooth skin texture during this dry season.