Go through these in order and stop at the first one that applies. If you are reading this for someone else, answer for them.
1
Is any of this happening now?
Call 911
Call emergency services or go to an emergency department if:
All or part of the finger has been amputated
Bleeding does not stop with firm pressure
The finger is pale, blue, cold, or suddenly numb
Bone is exposed or the finger is severely crushed
A ring is tightly trapped and circulation appears reduced
Other emergency signs, for anyone
Someone who is struggling to breathe, gasping, choking, or cannot get words out
Someone who has chest pain, tightness or pressure lasting more than a few minutes
Someone who has sudden weakness or drooping on one side of the face or body, slurred speech, or sudden confusion
Someone who is unconscious, or cannot be woken
Someone who is bleeding heavily and it will not stop with firm pressure
Someone who has had a seizure that will not stop, or does not wake up afterwards
Someone who has lips or skin that look pale, blue, grey or blotchy
Someone who you believe has taken an overdose or swallowed something poisonous
2
Is any of this happening?
Be seen today
Seek urgent medical assessment the same day if the finger is misshapen, cannot move normally, has a deep or gaping cut, or has a badly split or displaced nail.
Severe throbbing beneath the nail, suspected fracture, an animal or human bite, or contamination with soil may also need prompt care.
3
Does any of this apply?
Book an appointment
Arrange routine medical review if pain, swelling, or movement is not steadily improving, or if the nail later grows in a painful or troublesome way.
The article also says
If a fingertip has been amputated, do not scrub it.
Wrap it in clean, damp gauze, place it in a sealed waterproof bag, and keep that bag cool beside ice.
Do not place the body part directly on ice or in water.
Every sign above is quoted from the sofidex article on Smashed fingers. If you are not sure, err upward — it is always reasonable to be checked.