What are some exfoliants that are good for dry skin?

When I wear makeup, the dead skin around my mouth looks really flaky.

It's all white and flaky, I hate even looking at it.

So I ended up not really wearing foundation.

My skin is dry, so I just apply a lot of moisturizing cream.

Still, the dead skin cells and dry skin aren't getting better.

I want to exfoliate. Which product would be good?

The peeling gel is good, and the pads are good too.

Please recommend a peeling gel that is good for dry skin.