The following two lists are very helpful for anyone who is gluten sensitive and needs to avoid gluten when shopping.
It's very important to learn to read labels and understand sources of hidden gluten, and to know some general information about product labelling--for example in the USA if wheat is a possible allergen it must be declared on a product's ingredient label like this: Allergens: Wheat.
This may not be the cause, it's pure speculation on my part, but for 10-15 years I had a tingling/burning/electric-like shock sensation that emanated from my right-neck upward across the right-side of my head. I was worried about having a stroke or something so got all sorts of tests done, including an MRI, which found not much--only a minor degenerative disk in my neck--which I just accepted as the cause. Fast forward to when I was ~45 and I was hit with shingles in the EXACT place that this sensation would travel--I ended up with a very painful case of shingles that felt like the right-side of my head had been set on fire, and had the blistering and pain that ran along the exact path of nerves that I had felt this sensation travel along for the prior 10-15 years. For me, that time period was a shingles pre-cursor, and all those feelings were likely inflammation in my nerves. Needless to say I've not had this since getting my shingles vaccines at 50.
Your situation could very well be something else, but I just wanted to mention this possibility because your symptoms sound similar to what I experienced. I'm not sure if you're in the age range to get a shingles vaccine, but it may be something to consider.
Welcome to the celiac.com community, @Richard Rusnak!
The short answer is "No". Barley is a gluten-containing grain. The three gluten-containing grains are wheat, barley and rye.
Barley and rye contain less gluten than wheat but still should be avoided. Understand that smaller amounts of gluten may not produce a noticeable reaction in so far as symptoms go, but they still may be causing some inflammation in the gut. Products derived from gluten-containing grains should also be avoided, for instance malt and malt flavoring.