Hello, and thanks for your medical question on E Health Forum.
From the description of the pain, it seems that you might be having inflammation of the subcutaneous tissue of the finger.
You might benefit by using OTC analgesics like ibuprofen for a few days. In addition using icepacks on the fingers will be helpful.
In case the symptoms worsen, you might consult a doctor who can diagnose the exact cause and give specific therapy
I hope this helps.