I personally have never heard of a connection between SD (which is the resulting voice from the disorder technically known as laryngeal dystonia) and fibromyalgia. Like many conditions, I suppose they can co-exist but that doesn't mean one causes the other. SD is a neurological movement disorder.

When you say 'problems with your throat' do you actually mean with your voice? SD is a complex disorder, but a typical case only manifests itself when speaking, so under medical examination when the vocal cords are at rest your throat would appear normal.

Best wishes