What can treat itching eyes on the outside of the eye?

Cold compress: Likely allergy. Avoid eye makeup, or be sure to use a hypoallergenic product.

Depends!: Your question sounds like you are referring to the outer corners where the lids come together, the "skin". This area can often become irritated / chapped from excess upper lid skin or excessive tearing. I find it helpful with my patients to wash and dry the area twice a day a place a very thin coating of petroleum jelly there (vaseline).