I do not think it is GOUT as in gout pain usually stays in one joint and it is very severe and almost unbearable. Your condition is more like migratory polyarthralgia
. I would suggest you to get your Serum Ra factor, ESR and CRP. This will help us in guiding about diagnosis. You should take a indomethacin
like strong antiinflammatory and HCQ or SAAZ like drug also. Taking steroid
injection is not the right solution for it.