Rheumatology they physically check trigger points and your medical history to diagnose Fibro.
May suggest hydrotherapy but in the main they refer you back to you general practitioner
They don't offer treatment in UK.

That's because drugs treatment us offers here by your medical Dr
Rheumatoid is not the same as Fibro..pain wise it might be similar to fibro but it causes damage to the joints with redness and fever etc eventually it can result in deformity long term
Fibro is muscular no deformity .
Some poor souls have both conditions.

A rheumatologist or a pain management doctor both can treat fibro. Good luck

May I ask what do they do?

The rheumatologists here will only diagnosis fibro - they refuse to treat it. My internist and pain management clinic manage my fibro and do a really great job.

My neurologist treats my fibro but he said I could also see a rheumatologist that specializes in fibro (since not all are believers). Hope this helps!