As a general FYI because I have a friend dealing with an emergency right now, some airlines offer compassion fares or medical emergency or bereavement fares. If you have a family emergency and you need to fly right away, call the airline directly and ask.
They might require some proof like the name of the hospital/patient/funeral home but if you have to fly right this moment, it’s an option. The airlines might also allow you more flexibility on flight changes as well.
I know this applies for Delta, at least, and even if an airline doesn’t explicitly offer emergency fares, they may still be able to help you out.
Bereavement Fares are also offered on Air Canada. A lot of other airlines will be accommodating. On Air Canada, my family was treated well and they got us on the first possible flight.
Boosting.
Bootsrcool 