Answers:
Beer tannins could be one possible problem. More likely is an allergy to barley malt, hops, or brewer's yeast, although an allergy to brewer's yeast contained by someone who has no intolerance to baker's yeast would be extremely few and far between. You may want to have an allergy trial (skin prick test) to see what is causing the problem.
Other Answers:
If you own these effects from regular beer too you may be allergic to wheat products. I have a friend who is allergic to wheat. Try some whiskey newly to be sure.
"Non-alcoholic" still contains a tremendously small amount of alcohol. Check the label discreetly and you will see some listed (albeit a small amount). So, if you drink closely of it, you could end up beside a little buzz, especially if your tolerance is low (a well-mannered thing!).
As you can see surrounded by the chart below, you would have to consume almost 10 of the average near-beers to be equivalent to the alcohol in 1 regular average beer. Actually, it is probably even more than that, since adjectives the extra water within the 9 extra 12 oz beverages might further dilute the effect. That would be an interesting question for medical professionals... if you consume a beer and no other beverages, and later you consume a beer and say 4 pints of hose, how would your BAC level compare?
Beers/lagers/stouts/ciders , % Alcohol Content by Vol.
alcohol-free <0.05 0.04
low alcohol 0.05-1.2
standard strength 3.0-4.0
premium srength 5.0-6.0
super strength
8.0-11.0