What could little white spots under eyelids and face be?

Likely Milia: Without seeing you, it's difficult to say what your little white spots are under the eyelids and face. Commonly, small 1-2mm white bumps are usually milia, which are small cysts under the skin. Other while bumps include xanthelasma and syringomas. I would recommend that you see a dermatologist who will be able to evaluate these areas and treat them.

Rosacea?: Rosacea can cause small white bumps under the eyes and on the face, especially across the nose and cheeks.