Is this weather for real... I'm going crazy because of all the dead skin cells ㅠㅠ

As soon as the wind picked up and it got dry, dead skin cells started popping up around my mouth and nose—it's a total mess. Even slathering on moisturizer doesn't fix the inner dryness, and my makeup just cakes. In a situation like this, would it be better to just scrub at home, or would it be faster to just go to a dermatologist for a professional treatment? I just sigh in front of my vanity every morning, seriously.