Odds are against you
It sounds like you have no witnesses, nor did you try to report/pursue this matter immediately on arrival (before leaving the airport.) Your case may be similiar to workman's compensation cases where the employee loses because he failed to report the accident, to the employer, immediately.
Whatever you do, insist on a cash payment for your injury. Asking for miles or a free ticket (which are worthless things anyway) will make you sound like someone trying to rip-off the airline.
In any case, good luck.
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