Possibilities include atopic dermatitis (allergic problem) or ringworm. Patchy, flaky rash on the eyelids that seems to spread slowly is characteristic of ringworm. Only ringworm medication fixes a ringworm rash, so experimentation with antihistamine creams or steroid creams won't help. If you play basketball at a recreation center and use communal shower facilities you could easily have contracted it there. And some people just mysteriously get ringworm.
Before trying any home remedies, you should be evaluated by a dermatologist. Since this is a skin problem on the eyelids rather than an eye problem, I think a dermatologist would be the most efficient place to start.