You asked what you should do... That was my answer...
It’s almost impossible to diagnose something like this over the internet, and the majority of us here would be loath to do so.
My second answer you might like even less. Stop doing what you are doing if it is causing you pain.
And believe me... I am not being flippant here. I come from a decades long background in rock climbing and have experience more than my share of finger injuries. Something poorly, or misdiagnosed and resultantly mistreated can lead to chronic issues.
Rest-up and ice... see what happens...