Please recommend a good shampoo for removing dead skin cells from the scalp.

This is the shampoo I am currently using.

It's not that bad these days since it's summer, but in the dry winter, I tend to get flaky skin. In the summer, it's fine except for a bit of itching. I wash my hair every day.

But why do dead skin cells still form?

I tend to just buy cheap shampoo when it's on sale. Is it because I use it carelessly?

I should have been more mindful of my scalp when using it, but I think it might be because I used it carelessly.

I heard Head & Shoulders is famous for its dandruff shampoo and scalp exfoliation. Should I switch to that? What do you think?

Has anyone used it? Is it good?

Or please let me know if there are any other shampoos that are effective for exfoliating the scalp.

Would something like Nizoral also be effective for exfoliating the scalp?

I'm curious. Please let me know. ^^