What kind of doctor should I see for gout?

I was diagnosed w gout early summer and was referred to a kidney doctor (by my primary care dr.) due to a slight to moderate decrease in my kidney function (68yrs old). Primary care was prescribing 10, 10mg of prednisone on request, to take as needed for gout flare-ups which were happening every week. 10 tablets would last me 1-2 weeks and I would only take them as needed.
My kidney doctor replaced the 10mg of prednisone with a 4mg dosepk of methylprednisolone and the dosepk is working well. It is a 6 day regimen of taking 6 tablets on day 1, 5 on day two, 4 on day three and so on. Usually after the first 3 tablets on day one my flare-up is resolved. I followed the directions and took all 6 days for the first two dosekpks, but cut back on the third so I would have some on hand for flare-ups. My kidney doctor told me yesterday he shouldn't be the doctor to continue prescribing flare-up meds and that I should reach back out to my primary care doc or a rheumatologist. I've reached out to primary care doc to clarify. The allopurinol the kidney doc prescribed is slow to work - I've been taking it for 2 months and continue to have flare-ups between the prednisone and methylprednisolone. I've avoided all red meats, shellfish, organ meats, sweet drinks and am drinking at least 60 oz of water and a sugar-free drink (Powerade) daily that contains electrolytes. I have also avoided beer and wine, but have had an occasional bourbon over the last few months but not to excess. On days when I'm not in pain, I'm able to exercise (walk 2.5 miles in 45min) but those days are limited in number. I need to lose 20-30 pounds but is slow to accomplish when mobility is so limited.
My question is, should I seek a rheumatologist or stay with my primary care doctor for treatment? Any recommendations are appreciated. I should hear from my primary care doctor today or tomorrow but would like to hear recommendations based on anyone's actual experience.
Thanks in advance.
B Burris