Please recommend some cosmetics that are good for dead skin cells.

My son, who is now going through puberty, is getting severe dead skin cells on his face.

I'm not sure if I have dry or combination skin, but it seems to be getting worse because I don't apply cosmetics properly.

I hate the sticky feeling and find it bothersome, so I end up throwing away the cosmetics I bought after they expire.

Are there any products that are good for fresh exfoliation?