My mouth area is so dry ㅠㅠ Will at-home exfoliation definitely be effective?

Lately, I've been really worried because the skin around my mouth feels unusually dry and tight, as if it's cracking. No matter how much effort I put into applying my basic skincare products in the morning, after just a short while out, the corners of my mouth turn white and chapped, causing my makeup to clump and look messy. The more I touch up, the more the dead skin cells stand out, so I find myself constantly covering my mouth when speaking or smiling in front of people. It's really bothering me.

Given the situation, I am trying to exfoliate at home by myself, but since the skin around the mouth is so delicate, I am worried that using a scrub with granules might actually make it sting and turn redder. I am also afraid that I might accidentally damage the area and cause fine lines around my mouth to deepen or compromise my skin barrier. Are there any gentle, non-irritating exfoliation methods that people with sensitive skin like mine can practice at home?

I would like to ask for advice on whether there are any tips for achieving sufficient results with home care alone, or if it would be a much faster and more certain solution to visit a dermatologist and entrust professional exfoliation to an expert given the condition. I desperately need a secret method that gently soothes the unsightly crust while fully replenishing moisture, rather than just blindly peeling it off.

I would really appreciate it if you could share vivid personal experiences from those who have actually gone through similar symptoms and regained smooth mouth corners, or if you have any product recommendations or treatment information. I want to return to having soft, smooth skin where my makeup no longer cakes. I look forward to your valuable responses! Please help me!