Hello,
Emu oil is used in eczema just for moisturisation of the skin. Eczema can be exacerbated by dryness of the skin. So emu oil can be used for moisturization. So you have to use good quality moisturizers to prevent moisture loss from the skin.
Medical research shows that the most effective treatment plan for eczema involves using a combination of therapies to treat the skin and making lifestyle changes(prevention of triggers and application of lots of moisturizers) to control flare-ups.
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 dermatologist. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.