Can fibro really cause severe anxiety all alone, just from it?

Not generally: Many people with fibromyalgia also experience anxiety and depression, and having the chronic pain from fibro may intensify existing depression/anxiety. If having 'severe' anxiety, please see a psychiatrist. That may provide you the best assessment and help.

Could be associated: Best to explore source of anxiety with a psychiatrist or psychologist, as fibromyalgia may be made far worse due to your emotions. Recent evidence suggests that fibro not a mental illness whatsoever, and even depression lot less common than previously thought. So, get a good global approach with counseling, meds, exercise, stress management, etc.