Getting an earlier appt with rheumy

Hi, I saw my GP around 9 days ago as the pain and swelling in my joints was getting worse.
I had received a copy of a letter from them to my GP stating that they think my pain etc may not be well controlled due to the fact that I work as a childminder, so what would happen if they were my own babies??
My appt is for 5 March, but its so painful now, I cant sleep due to pain in hips and neck and shoulder, which is agony when I move. Last visit on 27 Nov, said to add another mtx pill, so up to 15mg and wait and see.
My GP thinks its not going to work if it hasnt by now, I started on mtx in July, and been back twice since then with 1 pill added both times.
I phoned them Friday and was told my appt available and that they need to speak to the manager. I called again today, and again no appts, but would put me through to the consultants secretary. I waited and waited, but no reply. I calleld back an hour later and found out she is off today, so can I call tomorrow. Ihave been advised to get a private consultation, but not sure how to go about it, also what the cost is likely to be. Any advice please?