Definitely go to the neurologist to see what's up, but don't be surprised if you do have NTOS if they don't find anything or tell you that NTOS doesn't exist. The "proper" specialist is a Vascular Surgeon and in some cases, a Thoracic Surgeon. Before you book an appointment with one, make sure to talk to their nurse and ask if they are familiar with TOS at all and how many people they see with it. Check out the featured post for a list of doctors in your area. It is not at all uncommon to have a completely normal EMG/Nerve Conduction Study with NTOS and for them to not find anything causing your symptoms. Best of luck to you and I hope your hand feels better soon!

Also check into the TOS center of New Jersey.
http://www.tosnj.com/Index.html

its PT and strengthening but it sounds like they have a good program. If you do let me know, I am interested in checking it out when I visit family in N.Y. You still need a real diagnosis though. For me the scalene block injection and the physical exam from 3 different dr's is what made it fairly conclusive for me although I also have a bulging disc and bone spurs.