What treatment should I use for pigmentation around the mouth?

I have previously shared my concerns about having a lot of dead skin cells and pigmentation.

What treatment should I get for pigmentation around the mouth?

It's right next to my mouth, so it's sensitive and my skin seems thin.

You can see that it tears easily

It seems like it would be different from hard areas like elbows or knees, but what kind of treatment would be good for the area around the mouth?

If anyone knows, please give me some advice.