What you are describing seems to be conjunctivitis ( an inflammation/infection of the area around the eyelid, commonly called pink eye in humans). This can be an extremely contagious condition which can spread not only to the swan's other eye but also to other waterfowl.

It is extremely important that you get the swan to a veterinarian to ensure that nothing worse is occurring, such as trauma from being poked or shot, etc. If it is conjunctivitis, the veterinarian will prescribe a veterinary antibiotic eye ointment which can quickly treat the condtion. The ointment needs to be placed on the eyelid once or twice daily. Ointment is better than eye drops because it stays on the eye and eyelid much longer in the water. Delay in treatment could possibly cause the swan to have sight problems in the future and worsening conditions, although rare, could result in blindness

The Regal Swan