How do you take care of dead skin cells on your lips?

Lately, unlike my skin which is shiny during the day, I am worried because my lips keep peeling.

I apply lip balm, but my lips get dry again, and there are times when I find myself touching them without even realizing it.

I try not to touch it as much as possible because I'm afraid I might unconsciously pick at it, but I just can't seem to manage it.

Due to the weather, I feel like my lips dry out more easily and peel frequently.

Are there any nourishing treatments available for this type of situation? I would appreciate it if you could share how you usually manage severe dead skin cells, any products that helped, or any tips for lip care before bed.