Tamaris, you have my sympathy.
As a fellow sufferer of extreme tiredness, I totally understand.
I can't get through the day without going back to bed for a couple of hours during the day.
At the moment I'm having my thyroid checked, I have a blood due this coming Friday.
You ask 'Is it worth going private' My answer would be yes if you can afford it.
I know of several people who have found out things by going private that wasn't picked up on the NHS and I for one am considering it. Good luck.