Non-refundable and non-changeable? Sounds like Priceline tickets...
Most tickets with discount fares will allow change with penalty, but when it states "non-changeable", it's another story.
You need some major exceptions to make airlines bend their rules. Some examples are: death of immediate family members, jury duty, army draft
Medical emergency is not one of them and it is only covered by trip cancellation insurance.
They were allowing exceptions for "fear of flying" after 9-11 few weeks ago. I don't think they are still doing that anymore.
The bottom line, no... it's not possible to change it.