Looking at the range of your symptoms and the distribution, the first thing that become obvious is the fact that it is a peripherial neuropathy, and that it involves the Brachial plexus.
Anatomically analysing this further means it is likely to be from C4-7, mostly the median nerve and the components of the radial nerve.
I am inclined to beleive it is not Reflex Sympathetic Dystrophy, which is mostly related to injuries and would have involved the whole hand rather than the thumb, index and middle fingers.
Pathophysiologically, your job, repetative motions involved would suggest either Carpal Tunnel Syndrome or an entrapment higher up in the Brachial plexus
So your neurologist must do an MRI of the neck, Nerve conduction studies as well as do a general check up CBC, Metabolic panel, endocrinology panels, and Autoimmune panels to rule out contributing co-morbid states
Fibromyalgia is not a near possibility. The pains are mostly generalized
I mst add, and you will be surprised to learn that except for CTS in which surgery might be considered as a last option. Treatment of the aformentioned conditions are similar