Well, in my opinion, it is fine to fly after you have got black eye. Generally speaking, people get black eye when there is injury to the eyes, even to the face and head, nose. It is just like you. And then the blood and other fluids collect in the space around the eye, and it will result in swelling and dark discoloration. But it is ok to take a flight. On the other hand, there are some ways you can have a try to treat your black eyes. For example, you can put some cold teabags under your eyes. In that way, the cold teabag can do a good job to your symptom. By the way, you can try using a cream containing vitamin D which can promote healing around the eye skin. Anyway, just be careful about it.