These dry patches can be due to dry skin or nummular dermatitis. The other possibility of such rashes is of atopic dermatitis. Although steroids, are commonly used for the treatment of atopic dermatitis, there are certain other agents also which are used like immune modulator drugs e.g. tacrolimus. These are available in the form of ointments and tend to prevent the recurrence. You can discuss with your dermatologist regarding the right use.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.