Depending on your symptoms, the main things I would want ruled out would be rheumatologic disorders so you're in a good spot with the rheumatologist. They'll likely do blood work to rule out, in addition to RA: lupus, polymyalgia rheumatica, thyroid disorders. You may want to ask if they evaluate for lyme disease as this is proving to be more common than previously realized. I wouldn't say this needs to be tested across the board, but if you are out in the woods regularly and are in a high frequency area it's definitely worth testing. STD testing would be wise if you're sexually active. Vitamin D, B12, and folate are also good to check as deficiencies there can be involved in some pain syndrome
Regarding heart tests, CT/MRI/sleep study: this depends on symptoms specific to you. If you have a predominance of chest pain, especially with breathing trouble then yes it's wise to get a cardiac eval. Sleep study....I would say that discuss your fatigue specific symptoms and perhaps look up the "epworth sleepiness scale" or a "sleep latency screen" if you screen strongly on those, take it in to show the rheumatologist to see if ruling out a primary sleep condition is necessary. CT/MRI: if there is a specific type of pain you're having that's isolated to one part of your body, shooting electric pain or you're having neurologic defecits then yes they should evaluate these. But if the pain is generalized throughout the body then the pain is more typical of fibromyalgia and those imaging tests are not neccessary.
Yes....fibromyalgia at this point is not curable. That's difficult to accept. BUT this is true of multiple medical conditions and that doesn't mean that there are not multiple ways to manage it and live a good life. If you want info on treatments medical and lifestyle, complementary etc, let me know, but I'll save that for another post!