What type of doctor can determine if I have had vagus nerve damage from lap band surgery?

Special Blood Test. Unfortunately, there is no 100% diagnostic test to confirm vagal nerve injury. Gastric emptying studies are often ordered but are notoriously unreliable. The best test is measurement of pancreatic polypeptide (pp) after Insulin administration. Normal secretion of pp is mediated by the vagus nerve in response to low blood sugar. If the vagus is injured, the pp level remains low after insulin.
Surgeon. Rare event. We see the nerves and wouldn't cut them. See your surgeon with your symptoms.
Neurological test. Your GI surgeon should be able to direct you to neurological testing to check it out.
Gastroenterologist. There is no good definitive test that i know of to diagnose a vagus nerve injury. However, a GI doctor may be the best one to determine if you likely have a nerve injury based on your history, symptoms, and other objective factors.