Can changing my hair loss shampoo change my scalp condition as well?

Lately, after washing my hair, I feel like my scalp gets oily more easily than before.

I was thinking about changing my shampoo, but since I was also worried about my hair thinning, I was even more confused about which product to choose.

Should choosing a shampoo based on scalp oiliness or itching be considered separately from identifying the cause of hair loss?

I am curious to know what criteria those of you who have switched products due to your scalp condition used to make your selection.