What is the best care for skin texture that has become slightly rough?

Lately, when I look at the skin on my cheeks and the sides of my nose, I don't have any major blemishes, but the surface feels slightly rougher than before.

It isn't severely bumpy to the touch, but since the skin isn't smooth and small pores and unevenness are visible all over, my face doesn't look clean.

At first, I thought it was due to a buildup of dead skin cells, so I tried using a peeling product, but it only made my skin soft for about a day, and if I used it frequently, it actually made my skin dry and sting.

I'm not sure if this is due to a lack of moisture or a loss of skin elasticity. Is it common to get skin boosters even with skin texture this rough?

I would like to naturally refine my overall skin texture rather than just making it temporarily moisturized, so I am wondering what kind of care would be suitable.