You've got a point, there, but I'm glad I'm not the only one who thinks my sister was being insensitive...she's called me oversensitive many times, and I'm beginning to believe her.
I've been trying to think about why it bothers me so much, but I'm still not sure - only things I can think of are that her singing replaces the song that's already in my head, and also that I have no control over what I'm listening to...plus, when she sings along to my favourite songs it means I can't hear them properly.

I'd love to be able to desensitise myself to her singing, but how would I go about doing that?

Singing along when we're in the car is a good idea, I'll see if I can try that for next time! And I could use my ipod in the mornings when she's singing along to the radio (I can hear it through the walls...I doubt she's even got it that loud, the walls in our house aren't very thick), hadn't thought of that before. Thanks for your suggestions!