I'm so sorry to hear about the medical issues in the house.
A lot of how we perceive the world is based on our expectations of it. That is, very few things are inherently "good" or "bad" or "annoying" - it's all how we view them.
So for example you currently view the singing and whistling as a bad thing. So it annoys you. However, lots of people would be thrilled to have people who sang and whistled, rather than sulked in silence. So see if you can reframe how you view it. Their singing and whistling is nice. It's their way of adding music to the world, like a bird singing its song. It's part of their song. It's a good thing that they sing and whistle. I love it when Bob walks around the house singing, it's a sign that he has positive energy within him.
It might take a little time, but it sounds like it's worth it, if it's part of your environment!
And consider, too, that they're both under stress with what is going on and maybe that is part of their stress coping mechanism. So when you hear it, think that they might be handling their own stress that way, and it's better to do that than to bottle it up.