Is there a lip care method that prevents dead skin cells from flaking?

I'm worried about dead skin on my lips.

Dry and cracked lips look bad, and I kept picking at them with my hands, so it hurt.

Sometimes it even bleeds, which is troublesome.

I'm upset because even when I apply lipstick, it doesn't look pretty due to the dry, flaky skin on my lips.

I want to maintain moist and smooth lips through consistent care. Are there any effective lip care methods to soothe dead skin cells and make lips hydrated?

For now, I just apply lip balm frequently.