Without seeing the swan's eye, we can only go by your description that it is pus. In this case, it may or may not be conjunctivitis which is similar to pink eye in humans. It is a bacterial infection that can be readily treated with an antibiotic optic ointment that can be prescribed by a veterinarian. We would suggest that you capture the swan and have the bird examined by a veterinarian to ensure that this is indeed the affliction. If left untreated, the other swans can catch this contagious condition and can make the swans miserable with scratchy itchy, runny eyes and the inability to see properly. The Regal Swan