In reply to DeaksClimbingLog:
It's very hard to tell of course over an online forum, but my (limited!) experience of pain in that area has been of a pulley tear, which has happened to me twice. In that case, does it hurt when you grip fully open handed? If not, while a crimp grip hurts, this could be pointing you down a line...
If it is this (and it's a punt on my part) - injury management for this kind of thing has moved on a lot in the past few years, and the wisdom now seems to be, keep climbing a low level, a level where it doesn't hurt. Your form and technique on the rock has to be good so the injury doesn't get stressed. You keep blood flowing into the fingers (helps recovery), but any accidental stress to the injury is a no-no.
All this assumes it's a particular type of injury similar to what I've experienced, which is may very well not be...
One thing I would say, is tiny tweaks happen from time to time, and if it's one of your first periods of finger pain, it might not be clear what an okay pain is and what a bad pain is. By 'ok pain' (since there really is no good pain in the fingers!) I mean something which is having a little moan now, but I know won't flare into anything bigger.
If in doubt, take some time away and come back to it over time. In the instance I mentioned above, my motivation disappeared for a couple of weeks (leave-it-the-hell-alone), then over a few sessions I worked back into it, slowly.