Really sorry to hear that. It's going to be a really tough time ahead.

If it were me I would call BA and put yourself at their mercy. Explain the situation and your need to get home as soon as possible for the reasons you outlined above and drop the routing you had with an ex-EU finish. If you can get a doctor's note I would hope you would be able to have all fees waived. It's not a right but they do do it in extreme circumstances like this. That's certainly what they did for me when I faced a similar situation (although mine didn't involve an ex-EU booking).

Good luck.