How to best manage an injury on the finger?

Swan-neck deformity indicates soft-tissue imbalance, tendon involvement, however it is unlikely after an acute injury. You should consult an orthopaedic surgeon who specialises in hand surgery or a plastic surgeon. You may need to immobilise your finger for 3-4 weeks with a finger splint to decrease pain and inflammation. You may need an x-ray to rule out any avulsion or bony injury then you should start with gradual physical therapy or exercises immersing your hand in warm water and putting it through a range of motion would make it comfortable.