Ours has done this and she had a chicken bone caught in her throat.
Why Do My Shih Tzu Keep Throwing Up Milky White Foam?
Its bile, probably caused by a hair stuck in the throat after grooming him/herself. Another cause could be your shih tzu is not getting enough fluids, as a dry throat can cause the same kind of tickle.
It probably just drank too much water.
My dog is spitting and gaging up white foam