Selective mutism currently is considered a variant of social anxiety; it appears to respond best to treatments for anxiety. I also would consider the hives and tearing up to be indicators that this is more than shyness.
There has also been some success with forms of video self-modeling therapy, the basic principle of which is to video the child speaking when comfortable (preferably in the target setting for future speech), and then have the child view themselves speaking. One can also edit video, to pair footage of someone asking the child a question with footage of them answering the question (not really at the same time, but edited to appear so).
