Fibromyalgia is a condition with many different symptoms of muscle pain and other problems. Many patients with fibromyalgia report headaches and neck pain. However, other things can cause these symptoms.
For example, infection, trauma, inflammation of arteries, and tension can cause headaches. Tumors, increased blood pressure, and bleeding inside the skull can also cause head pain. The key feature in your case is increased pain with neck flexion. This points more to a problem with the neck joints, muscles, or a nerve.
Don't assume all new symptoms are the result of your fibromyalgia. See your doctor if the headaches and neck pain don't go away in a reasonable amount of time.