--would indicate that your body is forming antibodies to gluten.

Of the usual celiac tests, the anti-gliadin is the most sensitive but least specific, generally; the anti-transglutaminase IgA is the test that is most often correlated with the villious damage of frank celiac, but not always.

There has been some research evidence, most specifically from European doctor Hadijvassiliou, that people with isolated anti-gliadin positives may show neurologic symptoms of gluten sensitivity well before they show any gastrointestinal symptoms, and they may even have a different genetic background than more classic celiacs. And, there has been some more recent research evidence that "non-celiac gluten sensitivity" is an actual thing, with distinctive immune markers:

http://gut.bmj.com/content/early/201...16-311964.full

It may be worth investigating further, as celiac is a known cause of neuropathy and other neurologic complications.