Lisa Rayburn felt dizzy, bloated and exhausted. Wynn Avocette suffered migraines and body aches. Stephanie Meade's 4-year-old daughter had constipation and threw temper tantrums.

All three tested negative for celiac disease, a severe intolerance to gluten, a protein found in wheat and other grains. But after their doctors ruled out other causes, all three adults did their own research and cut gluten—and saw the symptoms subside.

A...