I'll take it a step further on this basis to say that whilst all your pain is real, both fibromyalgia and RSI (99% of the time) are just labels given when those who gave them to you have no idea about TMS.
Like
@Rabscuttle said - fibromyalgia isn't really a diagnosis (as a diagnosis explains why something is happening, or at the very least the process which is causing the symptom) it's just a description of symptoms. Fibro means fibrous tissues (such as tendons and ligaments), myo means muscle, and algia means pain. So essentially what has happened is you've gone into the doctor's office and said "I've got widespread muscle pain" and then the doctor has gone away and said "Eureka, after lots of thought and all the tests you have, ready, widespread muscle pain!". He's repeated your symptoms back to you, but because it's in Greek/Latin it sounds super scary. If he did that in English (just repeated it back to you - which is what he did but in a different language), you would be like "well yes, obviously I know that as I'm the one experiencing it, but I want to know why?". It would mean nothing to you and it wouldn't help. Fibromyalgia means nothing as a diagnosis and as such doesn't really exist beyond simply explaining the symptoms (when auto-immune disorders, hormonal disorders and peripheral nerve disease have been ruled out that is - but if they weren't then you'd have another diagnosis anyway).
With RSI, in the absence of something more serious structurally (such as a tear), it's a similar story. I like to think of RSI in the same way as I think of the foot pain epidemic. We have the best footwear we've ever had and walk on better surfaces than any of our ancestors in history (they were walking on dirt trails and on jagged rocks), yet we are the ones suffering from chronic foot pain. It makes no sense. Likewise, there's an RSI epidemic from typing on computers, whereas people (not very long ago) used to literally spend the whole day (hours and hours, far more than most office jobs demand) typing on typewriters without break (which is far more onerous), and yet we are the ones with repetitive strain injuries. Food for thought.
I want to say also, we need to differentiate between TMS as a diagnosis and TMS as a treatment method. TMS is a diagnosis (albeit it comes with its own treatment method), it is not a standalone treatment method to treat structurally caused pain. It's not the case of I tried acupuncture, I tried physiotherapy, let me try TMS for my torn hamstring. TMS is the diagnosis, so you either have fibromyalgia (as I said above, no one really has fibromyalgia as it isn't a proper diagnosis) or you have TMS, it can't be both (a caveat - there can be mixed cases where pain is part structurally caused and part TMS, often in auto-immune conditions as an example, but this is rare and I highly doubt it applies in your case). Once you know you have TMS, then the treatment is unique. I say this because when you asked whether you can recover from Fibro and RSI using pain reprocessing therapy - if you meant can you recover from the symptoms themselves then yes - if they are TMS you can. If they are TMS, then that's what you have and the Fibro and RSI labels can be dropped
Hopefully that makes sense. let me know if not