Thanks for the query.
The finger needs to be examined. From your description of the wound, I presume it to be on the back of the finger and not on the palmar surface. If it is on the back of the finger, and you are not able to bend, it might need some simple physiotherapy
exercise to correct it.
The strings (Tendon) which help you bend and straighten the finger can get damaged when there is a cut. If it is cut, then it needs to be repaired by an orthopaedic surgeon
. To confirm whether there is any injury
to the tendon, you will need your finger to be examined. Please consult an orthopaedic surgeon for the evaluation and further treatment.
Hope I have answered your query. Let me know if I can assist you further.