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This is cherry eye, more properly known as eyelid protrusion or prolapsed gland of the third eyelid, is where the third eyelid is swollen in such a way that it become easily visible. It is called "cherry eye" because of the red color usually associated with the third eyelid when it becomes inflamed. It is believed to be congenital but the inheritance, if inherited, is unknown. Though it can occur in any dog, several breeds are prone to it, such as the bulldog, cocker spaniel, beagle, bloodhound, Lhasa Apso, and Shih Tzu. There is no known way to prevent the condition.
Treatment is fairly straightforward and often involves surgery to repair or occasionally remove the gland. Otherwise, anti-inflammatory medication will be prescribed to reduce the swelling.
Source is PetMD.