I get this from time to time, mostly in the winter, and per my dermatologist I use a very light touch of Eucerin Aquaphor, pat it in for overnight (more then) and for day I let it sit for awhile then dab off any excess with a tissue and continue with my usual eye cream and makeup. It really works.
Another gentle moisturizer is Norwegian formula hand cream by Neutrogena in the unscented formulation. It's thick too, so use a tiny amount and it does wonders, especially overnight, but also in the day as it is not oily.
Good luck! Mine is usually from an allergy to a product, especially eye shadows, mascara, liners, even concealers.