A little more information might help.
Is your cousin travelling with you?
Ordinarily I doubt they would consider a cousin going into hospital as a valid trigger for any of the medical exceptions unless they were actually travelling with you.
For the paid ticket what do the fare rules say about cancellations?
Often even with non-refundable tickets you can still change dates for a fee or cancel for a voucher less a fee so it may not be a total loss as long as you act before the travel date.