I too, was diagnosed with CFS prior to being tested for Lyme. In my opinion, CFS and fibromyalgia are "catch-all" diagnoses that doctors use when they can't or won't determine what is actually causing the condition. CFS and fibro have a symptom set that is common to a number of different chronic conditions, Lyme being just one of them.
The reason LLMDs are so highly recommended is because Lyme blood tests are antibody tests, and they can be incorrect 60% of the time. In other words, one may have Lyme disease, but the Lyme disease may not necessarily show up on the antibody test. Lyme sprirochetes are kind of like parasites, except that they change forms. This allows them to hide in the body. (Lyme sounds like it's something out of a sci-fi book, but it's real!) LLMDs are trained to diagnose Lyme not solely based on test results, but with attention to symptoms.
If you do have Lyme, mycoplasma, or one of the co-infections, it would make sense that you felt better while on the antibiotic. (Make sure they check for mycoplasma because it is often overlooked). Some people do well on long-term antibiotics, while others find that their symptoms return after they "finish" long-term treatment. Lyme spirochetes produce neurotoxins as a waste product, and some people benefit from treating the neurotoxins with herbals or with the prescription drug cholestyramine. These also help clear up brain fog.
There are two other possible contributors to fatigue outside of disease, assuming all your hormone levels are in order (thyroid, adrenal). Molds are a HUGE source of fatigue, and they're often overlooked in the home and workplace. I looked at 12 apartments in one college town, and I found mold problems in 11 of them. Basements (concrete slab), under sinks, in ductwork, or even in walls. Tests from the hardware store are not good for quantity, but will help you determine the type of mold. The schools I teach in have mold, too. The other contributor is electromagnetic radiation from cell towers, cell phones, wifi, and high power lines. To see where towers are, check: www.antennasearch.com.
I wish you the best!