Either "$10" or "10 [USD|AUD|etc]" are correct. It is unequivocally incorrect to use both symbols. use the first when it's clear in context what kind of dollar is being referred to, otherwise use the second.
That's going to need a citation. To be sure there's plenty of style guides which say "don't do that, do [this other variant instead]" but where's the standard that makes this unequivocal?