That's not good enough - and in my experience (physical health) you need to really chase up the NHS to get things done, or they will just forget about you. It shouldn't be the case but I've heard many people saying that you have to speak up. So do keep chasing them, get your GP to chase them, speak to PALS, lodge a complaint via NHS England.
Private may not be a bad idea - you could pay to get the tests and diagnostics done, then go to the NHS for treatment, as long as they accept a private Doctor's consultation letters.