For allergies/yeast infection you need an antifungal shampoo Ilike ketoconazole + chlorhexidine
If dealing with seborrhea then an anti sheborreaic shampoo like selsun blue or in some cases a coal tar shampoo works better but this general requires frequent bathing.
Dry skin that is no seborrhea hypoallergenic shampoo with moisturizer , oatmeal based shampoo.
Most critical part is a thorough rinse ie twice as long as you shampoo.
also a listerine or Vinegar rinse works well for yeast infections as well.