The best way to get a refund is to email or mail the ticket information to AA headquarters along with information about the surgery. It may take a few weeks but if the claim is legitimate, many people lie about circumstances, you should receive a refund, unless you have a nonrefundable ticket. I am not aware of a phone number that waits for passengers to call to ask for refunds. Here is a link
www.aa.com/customerrelations
I hope that helps.