Symptoms from Fibromyalgia can absolutely be disabling. If you are considering applying for SSI/SSDI, be sure to connect with a Rheumatologist who will document your symptoms (both physical and mental).
Social Security Administration adjudicators read your medical records and will want a clear picture of your functional limitations to prove that you are unable to work. The National Fibromyalgia Association offers resources and educational information for those dealing with this crippling autoimmune disorder:
Read this document for more detailed information.