Thanks for providing more information.
As per your description,possible differential diagnosis may include Gout,Degenerative arthritic changes,Nerve compression,Cervical spondylosis,Rheumatoid Arthritis.
So further a clinical examination by an Orthopedist and further bloodwork like CBC,RA factor,CRP,ANA,ESR,X-ray/MRI of cervical spine should be considered.
In my opinion,as you are already tried self medicines like painkillers which are not providing you relief so it's good to get prescribed medications as per underlying cause.
You shouldn't ignore and leave your symptoms untreated for a long period of time as they'll graduallt worse over the time.
You should soak your fingers in warm water for 10 minutes 2 times a day.
Keep your arm straight.
Avoid heavy weight lifting.
Hope this helps.
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