Yes, you can take the B12 on your own. We are very fortunate that B12 is safe, and high doses don't cause problems.

Without a test I'd start at 1mg a day of methylcobalamin the active form, and take on an empty stomach. About 13mcg of this will be absorbed even if you don't have active intrinsic factor.

You could have some compressive issue in your neck. Or at the thoracic outlet in the upper chest.

Here is our TOS forum that you can read and ask questions. Some doctors don't understand this disorder.
http://neurotalk.psychcentral.com/forum24.html

Carbamazepine can be toxic over time. It affects sodium levels, and can cause blood abnormalities. Were you tested for these issues?
http://emedicine.medscape.com/article/813654-overview
you may have to join medscape to view this article, but that is free and easy. It is very complete. Vasculitis, is listed as one sign of toxicity. This can affect the nerves.

Don't discontinue this drug yourself suddenly. It needs to be tapered off carefully. Discuss this with your doctor.