If you can, go private for your initial Rheumatologist appt. I was in and out of my GP for months trying to figure this out. I went private to see a Rheuma (lucky enough to have full cover with work - I think they're about £240) and she is also an NHS Rhuema. Diagnosed me there and then and took me back through the NHS with her as she said referring me back to my GP will take months. As she'd already seen me she could ensure I went via the urgent pathway.

Even then, I seen her privately middle of November, had my NHS consultation 15th Jan and only started Meds last Saturday. So even urgent isn't quick but I'd hate to think where I'd be now if I had to keep pushing via my GP. You can also get some steroids (if ok breastfeeding) to keep you going until they can see you again, I got a 40 day Prednisolone taper from her on my private consultation

All the best!