Fibromyalgia is classified as muscle pain and stiffness throughout the body along with sleep disturbances, hormone dysfunction, GI distburbances, and a range of other symptoms. I am not familiar with the IC diagnosis.
If you read through the health pages at the top right of the screen, you can learn a lot of information about treatment and underlying causes of Fibromyalgia.
As far as a diet for Fibromyalgia, it consists of a healthy diet of fruits, vegetables and for me, I only eat chicken or turkey and no red meat or pork. I also stay away from foods containing white flour and sugar as both promote inflammation. Problematic foods for some seem to be wheat, corn, milk and milk products and eggs. Also the elimination of MSG, aspartame, caffeine, and processed foods are important.