C.V.
Hi! Combat medic here. I don't have xray vision, but often the "kind" of pain can be a dead giveaway.
So:
Is it a ice-cold, poking, pinpointed pain that is in just one spot?
Or is it a hot/warm, aching, generally-in-this-area pain?
Based upon my experience, the ice-pokey-pinpointed pain is a break.
HOWEVER, if your pain has stayed at the same level over the past 3 days it's worth getting it looked at. With ice and rest, the swelling ought to have reduced. Even if it's a sprain, you might need to immobilize it.
ETA: Whoops! You say you hurt it last night? Okay. So...what kind of pain is it? ;-)
ETA2: I agree with JC, you can buddy tape your finger to immobilize it. That won't hurt. Please don't flick your fingertip to exacerbate the pain. Also, if your finger is noticably disfigured or "crooked" please go in for an xray. ♥