My DH's father used to do this for "patients"
as part of his practising of a thing called Radionics. Supposedly, he could diagnose people on the other side of the world by analysing a hair sample and then he could treat them with his little magic box, which manipulated energy fields in some way and sent healing out to people wherever they were.
It is the biggest load of rubbish that I have ever encountered. He thought that he could cure my pre-eclampsia, the boys autism, bed wetting, migraines (he had a patient who lived, literally, on the other side of the world for this one). He diagnosed my husband, who was under section in a psych ward, with selenium poisoning...
Please, please steer well clear of this quackery. it is absolute garbage and won't help you at all. There is no standardised methodology or reading of results, no indication of any kind that it is actually of any use at all and it can lead to people ignoring potentially serious medical problems.
The only proper use of hair analysis is forensic, where actual science is used. The other stuff is just mumbo jumbo.
I'm sorry that you don't feel well. I have ME so I now how awful chronic fatigue and all the accompanying symptoms can be, but hair analysis will not help you. Stick with your GP and, perhaps, look at your diet. Try cutting out caffeine and alcohol, eating more fruit and veg, getting some sunshine whenever possible, reducing white carbs and just trying to live within your limits. That'll help more than all the spooky guff under the sun.