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!