Red eyelid on corner of eye and very dry flaky skin on corner of eye. Treated with methylprednisotone aceponate but temporary effect, what to do?

Angular blepharitis. There is a distinct entity that affects the corners of the eye called angular blepharitis. It can be allergic/atopic in nature, but commonly can also be associated with bacterial infection and would require treatment with antibiotics. If steroids like Methylprednisolone aceponate have not helped, you should be re-evaluated by an eye md (ophthalmologist) for the necessity of antibiotic treatment.
Rash, or allergy. It may be from an allergy to chemical in shampoo, conditioner, facial soap, lotion, eye make-up, or an airborne allergy. As long as you get exposed to the chemical, the problem will persist. Patch testing by a dermatologist can identify the offending allergen. Then avoidance of the chemical, along with temporary use of a milder cortisone should clear up the problem.