Hello,
This dry skin of the ears can be due to xerosis or eczema.
The mainstay of management is liberal use of moisturizers after washing with luke warm water. Soap should be used minimally. Moisturizers should be reapplied liberally during the day.You can also use a topical cortisone (steroid) cream or ointment like dermacort(hydrocortisone). For the itching antihistaminics like Benadryl or Claritin can be taken.
If the symptoms are severe then it will be best to consult a dermatologist.Oral steroids may be needed.
I hope that helps. Take care and pls do keep me posted on how you are doing or if you have any additional doubts. Kind regards.
May be you have a fungal infection,could try canesten application.