I have to say that an expression indication mentioning a song bird with a tooth ache would certainly take a bit of pondering to pull off correctly !
Pooling the tooth out may turn out to be more of a practical problem.

Just one of the possible strategies: Let's say the mood is
doloroso = sorrowful (the bird is in pain, right?), which is a regular term in other music.
Your only problem now is to determine the quality of sound; still the beautiful sound of a singing nightingale or more of a squeak? Here you have artistic freedom, I think.
Paul