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It is likely to be from a sub-conjunctival hemorrhage.
In this condition the tiny blood vessels in the conjunctiva ( white part of the eye) get ruptured and bleed. It can occur under various circumstances such as excessive forceful coughing/sneezing, in hypertensive individuals, in those who are on blood thinning medicines such as low dose aspirin, following subtle eye injury or without any apparent reason too. It is self healing and will disappear within a week or two . I guess it is alright for you to catch a flight . The past history of iritis does not seem to be related to the present episode of burst vessel. Recurrent iritis would be associated with severe pain and photophobia along with the redness .
Once you reach your destination, you can start putting lubricating eye drops so as to soothe the eye. These are available OTC such as Refresh tears/Optive/Thera tears, 1 drop 4 times a day.
Do let me know if you have anything else to ask in this regard.
Have a good evening and happy flying!