I've had a similarly frustrating problem for the past 8 months. Constant peeling, redness and flaking lips. Tried Vasiline, Cortisone 1%, various chap sticks all with very little effect.
Finally tried an over the counter cream called Florasone Cream 10% Cardiospermum (found mine at Rite Aid). Noticible effect within 1 day and now symptoms are almost gone on the 3rd day. Cream says "For the temporary relief of itching & inflammation associated with minor skin irritations & rashes due to eczema, soaps, detergents, cosmetics & jewelry."
"In a 12 week study of 433 patients, 81.8% of these patients demonstrated significant improvement or disappearance of scaling and flaking skin."