Is there one simple test for fibromyalgia?

No. ? Whether is a test for fibromyalgia (FM). The answer is "no". The disorder is one of exclusion of other disorders with a similar symptom profile. Are some imaging studies (fMRI), blood, & physiological tests purporting to demonstrate changes seemingly correlate with FM, but they are not yet definitive. The best diagnostic instrument is doctor who believes in reality of FM & who has seen many.
No. There are no tests for fibromyalgia. Sometimes we will run tests to determine if other conditions that can look like fibromyalgia are present.
Hands-on. Not a blood test, imaging (x-ray, mri) test, or procedure (biopsy, EMG test). The test for fibromyalgia is the history and physical exam of a skilled physician who knows the diagnostic criteria for fibromyalgia. That exam includes palpation of the defined 'tender points' of fibromyalgia--you must have at least 11 of 18. You must also meet the other diagnostic criteria to have fibromyalgia.
Fibromyalgia. Have a full workup from your general care practitioner to determine if fibromyalgia is the correct diagnosis. If so, pain management, preferably with as few pills as possible is of utmost importance. Here is the website of the American Academy of Pain Management: