Well, yes, it is possible to have dry eyes because of fibromyalgia. As we know that fibromyalgia is a disorder whose most prominent characteristic is pain and tenderness at specific points in the musculoskeletal system. Also, other symptoms, such as hypothyroidism, certain viral infections, stress can accompany with it too. You should know that people with it will feel hard to sleep well, and they even feel tired. So in that way, it can just increase the eye pressure, leading to eye strain. Finally, dry eyes can occur. By the way, because of the stress on the eyes, red eyes, even dark circles, eye bags may occur too. So just pay more attention to it.
