Could I have fibromyalgia? What do I look for?

Dx by exclusion. This is a diagnosis when nothing esle applies. While 'tender points' are touted by many as part of the diagnostic criteria, but really are not. Talk to your doctor about your condition.
Widespread pain. ? What to look for to diagnose fibromyalgia (FM). Chronic widespread pain, depression, restless sleep & upper & lower back pain are common in FM. There are no laboratory or imaging studies to prove the diagnosis, which relies on physician instinct & intelligence to rule out other causes of symptom constellation being considered. Tis difficult to prove condition which is a negative; without proof.
It is common. Fibromyalgia is a chronic pain syndrome. There are 5 million people in the US who have fibromyalgia. People have widespread pain, tenderness with touching, can have poor sleep, can have problems with psychological issues. You need to discuss this with your physician and clarify your symptoms.