Is there a really good, moisturizing lip scrub to fix chapped and peeling lips?

Just out of the blue, my lips have started chapping. They feel really dry when I rub them together.

Out of the many lip balms I’ve tried, Carmex in a tube provides immediate relief, it does soften and moisten my lips right away, but that’s just a temporary fix. It doesn’t fix the dryness and chapping issue.

I’ve never had this issue before.

I thought about trying a lip scrub. What are some good ones to recommend?