Celiacs are people who can't metabolize gluten. They get really sick!
But I know a lot of other people who claim to have gluten 'intolerance', and many of them point out the same kinds of symptoms you have (plus headaches, joint pain, migraines, etc.). I don't think there's any medical understanding of this, but that doesn't mean it doesn't exist.
Why don't you try going gluten-free for a couple weeks or a month and see how that helps! If there's no change, then you know it wasn't gluten that was causing the symptoms.