Yes, you need to go to a private doctor if you are not getting the correct help and dx at the VA. What you described could be anything from a pinched nerve to MS to neuropathy , blood clot or many, many reasons. I'm sorry I don't buy the anxiety thing, but that's just my opinion and I'm not a doctor.. ,
First, IL is right, you should see a neurologist. I have many of the symptoms you describe and while yes, I have anxiety, I've also found out that a lot of the pain and tingling is due to my bite being off. When your teeth don't come together evenly, it can throw the rest of your body out of whack. I wonder if you had any dental work done while in the military? I would suggest seeing a dentist to check out TMJ. You may also have degenerative disk disease in your spine which can cause these symptoms as well. This will show up in an MRI.
I'm afraid once you've been dx'd with anxiety, it tends to be a catch all and dr's stop looking for other causes unless you ask for specific tests.
Some medications can cause temporary movement disorders but numbness is not part of that. If you are not taking any medications there might be another cause and that a doctor would have to determine it but I would get a second opinion just to be safe. There are a whole cluster of physical symptoms that can occur with anxiety but I would think that a full exam by a doctor and perhaps a neurologist to rule out any other physical conditions might be warranted and then they could make a further referral to a psychiatrist and then communicate with them from there what they found as regards a diagnosis.