. Eczema is a form of chronic dermatitis (rash).Allergic reaction is one of the important causes of eczema.
My sincere advice would be to consult a dermatologist and get it evaluated as treatment is diagnosis specific. Regarding the ear discharge, it can be due to otitis externa or otitis media. For this an ENT specialist’s consultation is required.
I hope it helps. Take care and please do keep me posted in case you have any additional doubts. Kind regards.