I'm sorry to hear you're going through a tough time.
Are you wanting another op because you think there's endo remaining? I'm assuming they removed endo during your two previous ops.
Have they suggested your pain could be due to scar tissue/adhesions?
What about asking your gp to refer you to a pain management course to learn strategies on how to cope with the pain?
It's incredibly difficult to balance the number of surgeries as the more surgeries you have the more scar tissue and adhesions and maybe that's why they're bringing your age into it? That's not to say they're right to do so but I'm trying to think of a reason why to refuse you surgery other than your age.
You can seek a second opinion and there is a list of all the accredited specialist endo centres on the BSGE website -
Have you looked at the Endo UK website? They have templates you can print off such as a pain diary. You can fill this in and then show your GP or gynae so they can see it in black and white the pain you're in. Or you can present it to the gastroenterologist when you have that appointment - although not sure why you're getting that referral!
I'm really very sorry to hear you've been through so much at such a young age. Please know the Endo UK Helpline is free and confidential should you need someone to talk to -
Take care x