In reply to markAut:
> Does this sound like pulley damage?
No. You would expect swelling at the underside of the fingers rather than the knuckles, generally more towards the base, or even see the flexor tendon pop out if you have a full tear of the annular ligament.
> What about bursitis
possibly, but would not tell you much about the cause even if confirmed, just that the inflammation in your joints also affects the bursae (fluid filled recesses).
> collateral ligament
On several fingers? Is pushing sideways against your outstretched finger tips painful?
> extensor ligament damage?
How would you get an overload injury on your extensors by climbing (these are for stretching your fingers!)
When I suffer from overload induced inflammation I generally complement resting with a short dose of OTC NSAIDs, e.g. Ibuprofen or Diclofenac. The rationale is that the inflammation is not only a response to damage incurred, but also by itself damages the tissue further and should be suppressed.
I would not do this if I regularly took NSAIDs for other reasons, but fortunately I do not suffer from headaches, so I believe my stomach and/or kidneys can cope with a few pills every few months...