What should I do about skin that breaks out every time the seasons change?

As the seasons change, my face has suddenly started stinging, and even the skincare products I usually use feel like they aren't sitting on the surface, so I'm worried.

White dead skin cells flak around my mouth and cheeks, causing my makeup to cake. However, I am hesitant to exfoliate because it makes my skin too sensitive. When I look in the mirror, my complexion looks dull and the unevenness stands out, so I don't even want to look.

I'm so frustrated wondering if it's just a matter of dehydration or if it has progressed to the stage of skin inflammation.

Is there an effective solution to fix skin that breaks out during the change of seasons?