Washing habits and strengthening the skin barrier

As the cold wind starts to blow, I'm worried because my skin gets red and stings after washing my face.

In particular, the area around my mouth and cheeks becomes so white and tight that my makeup keeps coming off.

I don't know if the temperature of my face wash is too high or if my cleansing product is too strong.

Please recommend some hypoallergenic cleansing tips or packs that can protect the sensitive winter skin barrier while maintaining moisture.