You have already cancelled, so anything you try now is going to be after the fact and an uphill battle I'm afraid. You can try to write in to SIA and supply the documents for the circumstances you were impacted by, but for starters you need to decide was it medical or compassionate as they don't quite seem to go with one another. If someone very close (immediate family) passed away, there may be an avenue to get some goodwill and maybe credit for future booking or such, but this would have been at least somewhat easier to work out before you cancelled and by doing so accepted the measly taxes refund and loss of fare part. They also may have agreed to a "courtesy" change or such, but again, before the ticket got cancelled.

usually for medical reasons (outside of past Covid policies), whether self or others (even for dependents) an airline does not have to care and that is what travel insurance would be for if your case meets the policies criteria (assuming you had / have one for that trip).

Good luck, but this could be a costly one I'm afraid.