My dead skin cells get really bad every late autumn. How should I manage this?

I'm worried because dead skin cells keep appearing on my cheeks and around my mouth as the weather has suddenly become dry lately. My skin feels tight after washing my face, and even if I apply multiple layers of basic skincare products, it feels rough again by the afternoon.

I am stressed because dead skin cells stand out even more, especially when I apply makeup. My foundation feels cakey and settles around my nose and mouth, so lately I have been keeping my makeup as thin as possible. However, I am hesitant to scrub indiscriminately because I worry that exfoliating too often will make my skin even more sensitive.

Seeing how my skin stings and turns red more easily than usual, I wonder if my skin barrier has weakened. At home, I've been focusing on using a mild cleanser and moisturizing cream, but it doesn't seem to be recovering as well as I expected.

I am wondering if it is advisable to start with soothing or moisturizing treatments at a dermatology clinic for skin like this in late autumn. I would appreciate it if you could let me know if there are any procedures that can be performed even when the skin barrier is sensitive, and what kind of treatment would be least burdensome to start with when the exfoliation is severe.