Doubt it's finger stick testing as no one pokes their fingers there do they? That should be done at the side of fingers.
Soak the finger in some hot salty water and give it a squeeze and or poke with a lancet to remove whatever is in it.
I would go to your gp and see if there's a foreign object stuck in underskin that is causing the inflammation, if there's nothing there it might be you'll need a course of antibiotics to clear it up.