What are some ways to get rid of eczema on my scalp?

Allergy or Derm eval. There are steroid based shampoos if you are certain you have eczema on your scalp and it is difficult to treat.
See Below. Dry scaly skin on the scalp can have multiple causes. Dandruff is the most common and scalp eczema is actually rare. Dandruff can be treated with otc dandruff shampoo. If this doesn't work, see you dermatologist. Other conditions such as psoriasis also have effective therapies.