I have psoriatic arthritis. I've had it for 33 years so I have had a lot of treatment.
I'm glad you have an appointment in the near future.
Things that can help. You need a stronger pain killer. Something a GP told me is that paracetamol alone is quite mild but strong when it is prescribed with other drugs eg codeine.
Naproxen is an anti-inflammatory, it worked really well for me but as I got older the GP stopped prescribing it as there are risks to taking it over a certain age.
As well as painkillers you need an autoinflammatory, your GP should be able to prescribe it.
Steroid injections in to particularly painful joints. I'm lucky my GP does them some people have to go to the hospital.
Heat / cold. This depend on how you feel, cold (ice packs) can reduce inflammation, heat can help with pain a hot water bottle or heated throw.
The drugs you have described are disease modifiers, I've had them both but also reacted so I am not on them at all now.
A TENS machine, in simple terms it confuses the nerves so the pain signal doesn't get to the brain. I was lent one by a physio, it worked so I bought my own.
Hot paraffin wax, this is great for hands, You probably need to see a physio to learn how to use it safely.
Hydrotherapy, preferably at a hydrotherapy pool with a physio but they will give you exercises to do at a local pool.
Physiotherapy.
Lastly a visit to an orthotist, they make various items made for you. For me it was some foam built up to put in my shoes and some 'resting splints' mine are for my hands, these are made to your size and in a position that is how your hands should be at rest. I use them for an hour in the evening.