What product is good for flaky lips?

Hi, I have flaky lips 365 days a year ㅠㅠ It's worse in the winter, but I have a lot of dead skin even in the summer.. So when I apply lipstick, it doesn't look pretty and just looks really messy, I guess..

I want to properly exfoliate my lips so that any lipstick looks pretty on me, but I'm not sure which products are good. The Sulwhasoo lip care products look decent, but I'm not sure what they are like.

Sisters, please help me..