What can I do to treat the pain of fibromyalgia but not be sleepy all the time?

Lots. The best treatment is regular sleep, routine exercise, and proper diet. Many who suffer from fibromyalgia pain have chronic persistent hyper-alertness with over stulation of the sympathtics. I routinely suggest mindfulness or meditation as part of the treatment. The right exercise that promotes proper breathing and mindfulness can be an excellent routine-qigong, tai chi or gentle yoga are great!
Exercise. Doing 30 minutes of aerobic exercise daily has been shown to improve pain from fibromyalgia and increase energy levels.