A rheumatologist would be the appropriate specialist for gout and a number of more or less similar joint problems. When it comes to diagnosing gout or gout-specific therapies like allopurinol, rheumatologists are the most experienced. For foot symptoms though, you needn’t see a rheumatologists.
I don’t know what’s expensive and what’s not in your country but other specialties routinely deal with patients’ foot problems and help with symptoms.
You apparently have significantly higher uric acid than Clement. So I’m not sure you’re dissolving a great many crystals yet.
And I would expect symptoms caused by crystal dissolution not to be so long-lasting and to include redness and pain. But maybe your body works differently…