I have eczema, but it's stress-related rather than allergy related.

Liberal application of hand cream (foot cream is even better) after I wash my hands. And in between. I've put mini bottles of lotion in my purse, next to the bathroom and kitchen sinks, backpack, etc for any time they feel a bit dry, especially after using the evil institutional soap. What are your gloves made out of? Fleece and even Thinsulate linings suck moisture right out of my skin.

Hydration is also important. I've got electric baseboard heating (hate it!) and it dries the place out. It's like living in poorly-insulated toaster.