@fBoyle-- Yes, fibromyalgia can cause both nausea and weakness. I have both, as well as headaches and muscle cramps. I think that nausea is a very common fibromyalgia symptom. Most people I've spoken to about fibromyalgia have mentioned it.
Fibromyalgia is such a complicated disorder. No one knows the exact cause and there are probably different types of causes. That's why symptoms can vary a little bit from person to person but pain and fatigue seem to be common for everyone.
Have you been diagnosed with fibromyalgia? Chronic fatigue syndrome, which is a different disorder, can cause these symptoms too.