When should I seek medical attention for a severe finger jam?

Great pain; crooked. Treatment for a jammed finger includes: rest, cold packs, & elevating that hand up to the chest. Motrin or Advil (ibuprofen) for 3 days helps reduce the swelling & pain. One can "buddy splint" by taping the injured finger to the finger next to it for a few days. If the pain is severe, the finger crooked, or the range of motion significantly decreased, a primary or orthopedic doctor can evaluate & do an x-ray.
ASAP. See your doctor or orthopedist as soon as possible for severe jammed digits.