I have a friend whose son has been diagnosed with selective mutism. It is definitely not shyness, and "selective" is a misnomer, he cannot talk in class, period- it is not selective which implies a choice. He is a chatterbox at home however.

If your daughter has this much anxiety with speaking, whether or not she actually has SM or some other kind of anxiety issue, she needs help- I definitely recommend talking to a developmental psychiatrist.