Just be aware that if you stop eating gluten and have to go back on to it to have the endoscopy for a proper diagnosis, then the symptoms may be even worse.
There are advantages to a proper diagnosis and whilst they are there a proper check to see if there is anything else wrong. Also, there is more support from the NHS for further checkups, dietitian, bone density scans, routine blood tests, letters to get more baggage allowance for your GF food on planes, etc. You may be able to talk your GP into giving a diagnosis without an endoscopy though.
You should talk to your GP about this. The blood test results will typically take 2 weeks.
The wait for an endoscopy could be 4-12 weeks (once you are put down for it by the consultant at an appointment).
You can speed up seeing the consultant by having a private appointment if you can find the money for it (about £150 perhaps) or get your GP to say that it is urgent and ring up and say that you will take a cancellation.