Well, generally speaking, you are not supposed to have plane when you have eye infection. First, you should know that if you take airplane with eye infection, it will make your eyes become worse. In common, when you are in the plane, your eyes have to face some problems because of the gravity. And that will lead to eye strain. And that will just make your infected eyes get more serious, leading to some eye diseases. So you need to pay more attention to it.
Eye infection may lead to pink eye. It is common to get such disease infectious conjunctivitis. It is an acute infectious eye inflammation which possibly infected through articles contacts of patients. You may allowed to take plane, but it is easy to infected through articles contacts of patients, including used towels, door knobs, water faucets, swimming pool water, public toys etc. This disease would happen all the year around but especially find more in spring and summer in public places. However, it is spread by touch but not by air, pay attention no to touch the public staff or other people, nothing serious for you to take plane. Take care to your personal eyes hygiene to avoid infection again in public places, take eye drops with you; that is OK!