We all are different in our treatments and the results. I respond to cold tar shampoo.

Shampoos containing antifungal agents like ketoconazole, selenium sulfide, or zinc pyrithione are effective for treating an itchy scalp caused by seborrheic dermatitis. It's also important to choose products free from harsh ingredients like parabens and sulfates to avoid further irritation.
Business Insider Wikipedia
Recommended Shampoos for Itchy Scalp Due to Seborrheic Dermatitis
Key Ingredients to Look For
When selecting a shampoo for seborrheic dermatitis, focus on those containing antifungal and soothing ingredients. Here are some effective options:
SHAMPOO ACTIVE INGREDIENT BENEFITS
Vanicream Free & Clear Medicated Shampoo Zinc Pyrithione Antifungal, free of sulfates and parabens, gentle on sensitive skin.
Nizoral A-D Ketoconazole Effective antifungal, helps reduce flaking and itching.
Head & Shoulders Clinical Strength Selenium Sulfide Targets dandruff and helps control scalp irritation.
Selsun Blue Selenium Sulfide Reduces scaling and inflammation on the scalp.
DHS Tar Coal Tar Helps reduce itching and scaling, effective for chronic conditions.
Usage Tips
Frequency: Use medicated shampoos 2-3 times a week or as directed. Allow the shampoo to sit on the scalp for a few minutes before rinsing.
Alternating Products: If one shampoo loses effectiveness, consider alternating between different types to maintain results.
Avoid Irritants: Choose shampoos free from parabens, sulfates, and fragrances to minimize irritation.
Additional Care
In addition to using the right shampoo, maintain a regular washing routine to prevent buildup of oils and flakes. If symptoms persist, consult a healthcare provider for further treatment options.