Hmmmm...... you'll have to excuse my for this is more a collection of thoughts then well organised.
CRPS is a frequent dumping ground diagnosis for things consultants aren't sure about. Yy to making sure its not a miss diagnosis. The painkillers dont work should not be a criteria for diagnosis. Painkillers dont really work for joint hypermobility either for example. Juvenile arthritis is another common actual diagnosis.
Things to look out for in actual CRPS: extreme skin discoloration, hair growth places where hairs shouldn't typically be, extreme sensitivity to touch (no clothing), sensitivity to sound (yes really), sensitivity to vibrations, sensitivity to hot and cold, swelling, bizarre "at rest" angles. And there will be the unproposing small injury at the start. "Real" CRPS is very very visible. You will be sitting will your affected somewhat grotesque looking limb uncovered!. As you haven't mentioned any of this I would wonder whether tge diagnosis is correct.
Look into Oxygen tank therapy. I do know some people who recovered through this. Its not recognised by NHS (Or Bath who tell you no one recovers from it) and it is expensive.
Otherwise you are looking at any kind of pain killing that allows you to keep moving (and yes sadly that includes Bath's Psychological approach).
I had painkilling interguinethidine blocks. They were horrific and traumatic but allowed me 4-5 days completely pain free to Regain mobility and stay mobile until it went into remission. At the time (20 yearsish ago) the NHS only offered 8, I ended up having in the region of 40 most under anaesthetic or sedation over a period of 18 months from 11-12 years, then the RSD (as it was called then) went just dissappeared. Touch wood I haven't had relapse. I dont think NHS offer them anymore and Bath certainly won't. It was a private consultant Dr Wedley (who consistently got people better) but i think he and his approach is probably long retired by now.
You must must must keep moving no matter how much pain you are in. A physio who understands this and is able to work within your pain levels is invaluable. You are looking for one who can gently stretch your limits not smash them.
Spending time in/moving to a hot country can also help.
Swimming was diabolically bad for me at the start as I could not tolerate the touch of water.
And yes people do recover from it. Not many and as i hear it not many from Bath. As a teen your chances are better. and the more you can keep it moving the better your chances.
My mum ran a support group and national conference while it existed. We still see the little red book pop up every now and then.