There's no right/wrong about either your request or her feelings about the subject. You are allowed to want what you want and she's allowed to feel as she does about "singing." I'd say it was insensitive of her to insist on singing in your presence after you shared with her your dislike of it but she's allowed to choose to be insensitive!

I can't imagine she sings 100% of the time you are in each others presence? Were I you, I'd try to get to the bottom of why her singing bothers me so much and/or work on desensitizing myself to it. Maybe if you sang along with her something different would result? Carry around earphones/a radio/cassette tapes or something when she's near in case you're stuck and don't wish to listen.

Is there anything your sister would like that you could "trade" her for not singing in your presence sometimes? What do your parents say/think of the situation? Is this you all's usual behavior toward one another?