Well, I can see that you are quite worried about the risk of getting pink eyes from other people. Don't worry. In fact, pink eyes are primarily transmitted through direct contact or the contact with the patient's things. Generally speaking, the coughing would not transmit pink eyes through salivate. However, you still have to be careful not to get that into your eyes. Try to stay away from the patients' things and avoid direct contact.
As we all know, Pink eye is also named conjunctivitis and viral and bacterial are most commonly the causes of conjunctivitis. So it is possible that pin eye can spread through coughing. A doctor, who told me that conjunctivitis, or pink eye has several types and viral conjunctivitis and bacteria conjunctivitis are the two typical kinds. While when some get cold, virus and bacteria can get out of our bodies by coughing, so it is easy to spread in the air. Then these viral and bacterial may enter your eyes by chance. By the way, pink eyes may also get worse when you swim in a swimming pool. So swimming pool is also a high rate of getting pink eye.