Absolutely, fibro could be a possibility. Of course, so could a whole array of autoimmune illnesses, and so could your hypothyroidism. But an internist can check the tender points and so other analyses; if he can't, might be time for a new doc!
One thing you might do when you see him is take with you a diagram of where the tender points exist. If you go to the National Fibromyalgia Association Web site (fmaware [***] org), click on "About Fibromyalgia," and then click on "What are the symptoms?" it'll take you to a page that you can print out. It has a whole list of symptoms, and if you scroll down the page, you'll see a really great diagram of the tender points. Print it, take it with you, and then your doc knows exactlhy where to check.