My hands have really bad calluses. Is there anything I can do?

I have combination skin, so my face is oily

I tend to have it.

The problem with dead skin cells is severe right now, during the change of seasons. The dead skin around and under my nails is not just flaking, but actually peeling off. I can't avoid touching water, and even though I apply hand cream frequently, it doesn't seem to have much effect. Every time I touch my fingers, they feel unpleasant and rough.

Is there no way to get rid of dead skin on my hands other than hand cream? I really want to have soft hands.

Please let me know if you have any tips or good cosmetics.