There are several conditions that coexist with FM and CFS that can cause lightheadedness. Even more significant is research that suggests both POTS and NMH occur more frequently in chronic fatigue syndrome and fibromyalgia. Postural orthostatic tachycardia (POTS) and neutrally mediated hypotension (NMH) can cause extreme dizziness and alter one's ability to function. Both are treated by increasing blood volume with hydration and possibly a medication to help the body conserve its water.
Dizziness can mean many things and is not a symptom to take lightly. If you experience this symptom discuss it with your doctor so the appropriate tests can be ordered to determine the cause. If dizziness comes on suddenly, seek immediate treatment.