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I am Dr. Sohaib, a practicing Internal Medicine Specialist and i will do my best to help you today.
Excellent question you have asked Lisa.
Actually, whether or not he should take the flight depends upon the diagnosis (underlying disease responsible for the swelling of the eye).
In general, he should have examination of back of eye done, in addition to the CT scan report and thyroid tests to make sure there is no increase in intracranial pressure (which is expected to be high if the bulging of eye is due to tumor).
He can have some side effects due to flight and pressure changes such as he would probably be experiencing headaches and perhaps nausea although some people may not have any symptoms.
Havind raised intracranial pressure can lead to intracranial bleed, which can be serious, so it would be still best for him to clear his flight with the surgeon (in case of tumor).
With out approval from the treating doctor, he should not take the flight.
Right now, he should wait for the CT scan results, and in case this turns out to be some thing sinister (like a tumor), he would require a complete check up (pulse, bp check up, examination of eye) with out which he should not take any flight.
I hope this clarifies and answers your question.
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