Though black eye is commonly caused due to an injury to the face, sometimes, a black eye may indicate a more extensive injury, even a skull fracture
The reason of concern in this situation is presence of air inside the cranium (skull) including the facial bones.
This entrapped air tends to expand on ascending to high altitude (such as during air travel) & cause severe pain
In this regard, will be important to observe for 4-5 days & see if there is any aggravation of symptoms.
You have mentioned in your post that you didn't have any symptoms of dizziness
, blurred vision
or nausea...so it indicates a favourable prognosis & a flight may be taken.
But it is always better to consult the Doctor & get a proper physical examination done to prevent occurrence of any discomfort during flight.
Wishing a Good Health. Let me know if I need to clarify further.
Thanks & take care.