Pursue the coeliac disease route first, dince you have family history of it. Did the GP write that into your notes?
Rather than completely ditching the GP you otherwise trust, find out if your surgery has an "any doctor" policy. Try before you buy, so to speak.
Chronic Fatigue is an umbrella term for one of a series of (mostly) auto-immune disorders. My staff welfare officer got me to ask my GP to refer me to the Louise Coote Centre, St. Thomas' Hospital, Southwark. It took three GP visits to persuade my GP who, I suspect, had me down as a hypochondriac, to give me a referral to see their specialists. I got a diagnosis but you gave to go back every 12 months to report progress with the prescribed medicine. I only revisited once before the rail fare to London became unaffordable (I was too tired to travel, in any event).
Anyway, the hazard with horrible conditions like this is that, if the GP sees you more than about three times in any given year, they start guving you short shrift, like you are some kind of shirker. Mine wouldn't even allow me to get my lower back x-rayed. Thanks to fakers, I've had to put up with chronic pain for 20-odd years.
GPs prescribing anti-depressants is a new concept to me. Not so long ago you had to be referred to a psychiatrist first.
Suicidality warning: possibly rooted in cases whereby patients were too physically tired to get out of the house. Given prozac, they're restored to full mobility but they then use that to jump off a bridge, as if they've planned that for months. Truth is that it triggers all kinds of impulsive behaviour. I asked for it, once but was declined (same GP as above!)
They run campaigns trying to get men to report symptoms to GP sooner but, with uncooperative docs like mine was, is it any wonder we stop bothering?