This is a difficult question. You very well could have both. Since there is a more or less standard test for FM (tender points) and because FM is better known (and better regarded) in the physician community than CFS or 'ME" its possible that your physician didn't know enough to diagnose ME.

It may not actually matter.  A top ME/CFS/FM physician Dr. Lucinda Bateman believes most people with these diseases have degrees of each; some have more pure FM and some have more pure CFS and alot of people are in the middle. Pain is more prevalent in FM and fatigue is in CFS but both, interestingly, often have an infectious onset. THe most important thing is getting good treatment from a doctor who knows about both.

For more on FM check out Health Centrals FM website, which I believe has a page on the differences between the two diseases

http://www.healthcentral.com/chronic-pain/fibromyalgia.html