Becks is brewed with barley malt, which does contain gluten.
I have the same problem. I'm not exactly Celiacs, but have a low tolerance for gluten. For instance, Bread and pasta make me break out in a rash and have some gastro-intestinal issues, but some more processed forms of gluten seem to be ok in moderation.
That said, I've found that the more delicious beers affect me if I have more than one or two within a few day span (Sam Adams, Harpoon, imports, etc.).
Through experimentation, I've found that Miller, Budweiser and Guinness are much more tolerable to me than the craft or import beers. I presume that light beers would be tolerable as well, but like the gluten-free beers available, I just don't enjoy the flavor of light beer.
Hope that helps!