The medical name for “cradle cap” is seborrheic dermatitis. It is very common in infants. The exact cause is not known. Possibly some of these factors play a role:
Your question about getting “rid of it” isn’t easy to answer without being able to see your child’s rash. Besides, it’s always important to know if you are seeing the rash only on the scalp or elsewhere on the body too. Of course, no one ever likes the way the red, scaly areas look or how the itchiness feels.
While the remedies you’ve tried can be effective, corticosteroid ointments or antifungal shampoos are necessary for some people. Your child’s doctor would be in the best position to prescribe these medications.
Making an appointment with the doctor would be a good idea, because the rash may not be caused by seborrheic dermatitis. It might be an infection (fungal or bacterial), eczema, psoriasis, another skin condition, or even head lice. Your doctor can take a good look, maybe do some tests on scrapings from the skin, and figure out how to best get rid of the problem. If all of these things don’t work, your child may benefit from an evaluation by a skin specialist (dermatologist).