Dandruff shampoo are classified:
1: Pyrithione zinc shampoo( DermaZinc, head & shoulders, others) these contain antibacterial and anti fungal agent zinc pyrithione.
2: Tar-based shampoos ( Neutrogena T/ Gel, scalp 18 Coal Tar shampoo, others) Coal tar slows how quickly skin cells die and flake off. If you have light-colored hair, shampoo may cause discoloration. It also make scalp more sensitive to sunlight.
3: Selenium sulfide shampoos(head& shoulders intensive, Selsun blue, others) anti fungal agent. Rinse well, as it can discolor the hair and scalp.
4: Ketoconazole shampoos (nizoral, anti dandruff) kill dandruff causing fungus that lives in your scalp.
5: Fluocinolone shampoos (capex, Derma-smoothe/FS, others) contains corticosteroids to help control itching, flaking and irritation.
Try these and it you see improvement, use less frequently for maintenance and prevention.
If you don’t see improvement, I strongly recommend seeing a dermatologist.