Suggest Treatment For Sharp Pain In The Head And Under The Eye
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Detailed Answer:
I read your question carefully and I understand your concern.
Judging from the location sinusitis is a possibility, it would correspond to inflammation of the left frontal sinus. However usually there is also nasal congestion and discharge, so if there is none of that I would have my doubts. Anyway there is no reason to fear from flying with an infected sinus, there isn't any added danger.
Another possibility would be tension type headache. It is the most common type of primary headache (primary meaning with no identifiable cause). Often is triggered by stress and anxiety. The fact that it increases as the day goes along would be in its favor. Treatment would be with medication like Advil which you mention and only if it persists over a month at least preventive treatment with amitriptyline may be considered.
As for cluster headache which you mention it is unlikely, usually it is accompanied by phenomena such as red eye, tearing, drooping eyelid, blocked nostril on that side. The pain comes in episodes of 15 min to 3 hours.
At times the cause is difficult to be pinpointed in such type of headaches, however you should feel reassured that judging from the current symptoms there is no indication of any alarming issue.
I remain at your disposal for other questions.