I hope you can see a vascular surgeon who is well-versed in the field of Thoracic Outlet Syndrome.
There is a list of doctors who specialize in TOS and are part of the TOS Consortium here; my surgeon is not on this list but he has done over 200 surgeries for TOS. That is a good thing to ask, how many TOS surgeries he/she has done.
http://surgerydept.wustl.edu/TOS_Consortium.aspx
You mentioned your doctor was in the military. I think there are many competent surgeons in the military but there are many more who specialize in TOS surgery who are not in the military.
Good luck!!