The outside corner of both eyes burns and is a constant burning and is irritated even more when touched or if anything is applied to it, why?

Eyelid pain. Almost all the causes are fairly innocent, superficial, and treatable. Dry eyes, inflammation of the eyelash oil glands, and and granulated eyelashes (blepharitis) make up about 95% of the causes. ..Each is different and each needs a proper diagnosis and treatment, usually drops and gentle warm wash cloth friction...Keep us posted...Dr. Sibley.