Can you explain if it's possible that my eyes sting from crying to much?

Usually not: Crying too much actually increases the moisture of the eyes, as well as increases the swelling of the eyelids. So usually crying doesn't cause stinging of the eyes. However, if you have a dry eye meibomian glands' oil layer of the tear film isn't adequate, then you might have tears that don't stay on the surface of the eye long enough, and can have a dry eye condition afterwards needing treatment.

Probably not: The tears produced during crying are similar to those made during "reflex tearing". In this situation, the eyes tear profusely if something gets into the eye or if it is injured or severely dry. These tears are not the most lubricating, and do indeed burn. However, the symptom of stinging would be much more commonly from dry eye, ocular allergy, or blepharitis as the underlying cause.