Please recommend a shampoo for itchy scalp.

I have a habit of scratching my scalp frequently because it itches.

I scratched it, so I got a wound, and as a scab formed, it got itchy again, creating a vicious cycle.

I go about my daily life by pressing firmly and avoiding scratching as much as possible.

Could this be because of the shampoo?

I have oily skin, so if I don't wash my hair once a day, it feels greasy.

I thought my scalp was oily, but every time I go to the hair salon, I am told that I have a dry scalp.

What shampoo would you recommend?