My skin is severely dry from within and flaky. What kind of care would be best?

As November begins, cold winds blow in the mornings and evenings, and with the start of indoor heating, I can feel my skin drying out rapidly. Immediately after washing my face, my entire face feels incredibly tight, as if it is tearing apart. Even applying a generous amount of my usual moisturizer doesn't resolve the inner dryness at all. Furthermore, white flakes of dead skin are flaking around my nose and cheeks, causing my makeup to clump and flake off every morning. I am worried that using harsh scrubs might further damage my already sensitive skin barrier, so I am curious about home care methods that can gently exfoliate without irritation. I am also considering skin booster treatments like LDM Waterdrop Lifting or Rejuran Healer to replenish moisture deep within the skin. I would appreciate your recommendations on which care is most effective for my current skin condition.