yes. Dr. A.S. Desai: Swelling of the white part of the eye(conjunctiva) is called conjunctival chemosis. It is just an edema due to excessive rubbing of the eye. It should subside on its own within a day or two.As long as there is no redness/pain or watering in that eye, the chemosis does not need any specific treatment.es. Dr. A.S. Desai: Swelling of the white part of the eye(conjunctiva) is called conjunctival chemosis. It is just an edema due to excessive rubbing of the eye. It should subside on its own within a day or two.