--what the doctor did with you is actually fairly logical, but it certainly isn't the only way to go, as many of the other respondents here are indicating.

What you have described sounds like neuropathic pain, which is differnt from regular nociceptive pain; it is generated by erroneous signals from compromised nerves (not accurately signalling nerves indicating other tissue damage). In such cases, the first line of medication often IS an anti-seizure drug, as many of these are often used to stop or lessen erroneous signal patterns from damaged nerves. (The most commonly prescribed of these drugs is Neurontin, or gabapentin, followed by the newer Lyrica, or Pregabalin). Anti-depressants, such as Elavil, are also often prescribed, as, at lower doses than used to relieve depression, they alter neurotransmitter balance in the nerves enough to have an effect on the erroneous signalling.

Still, a search for the CAUSE of your symptoms is very important. Given the location of your symptoms, problems in the cervical spine nerve roots, problems farther down in the shoulder upper arm (such as Thoracic Outlet), and even farther down the arm at the level of elbow or wrist are all possibilities, as nerves can be entrapped/compresses at any/all these locations.

You do need compreshensive imaging from the neck down, and possibly some nerve conduction studies, to try to pinpoint just what is generating the symptoms. Then you can plan on a therapeutic course of action, which may include medications but also physical therapy, exercise, perhaps, in extreme cases, even surgery.