Well, as a matter of fact, pink eyes is not as serious problem as you imagine, yes indeed, sometimes it would lead to some uncomfortable feelings and make you appear not that attractive anymore. it simply does not impede your taking a plane for an urgent meeting,however it would be contagious and transmit to other people .Therefore, I advise that you just pay more attention and do not let it transmit , get some treatment before it becomes more serious.
You can't go to there by plane. The pink eyes is a contagious disease, that means you may transfer it to other passengers. Then, you must take some medicine and style at home til your eyes clear. That because the dry air on board may aggravate your illness. So, I think you just stay at home.