I keep getting dead skin cells on my lips even after applying lip balm. Why is that?

My lips are in really bad condition these days.

Even though I apply lip balm frequently, my lips remain dry and flaky.

Even though I intentionally use a moisturizing lipstick because it's summer

When I apply lip tint, the color gets stuck in the dead skin cells, making my lips look even messier...

I also tried applying Vaseline before bed.
It was exactly the same again in the morning...

I also tried Paw Paw, which is famous as the flight attendant lip balm... Ha

But it didn't work.

Are there any good products to use when your lips are very dry and flaky?