Is what happened by changing the shape of the nose considered a sin that necessitates repentance, or is it permissible to sue the doctor despite the passage of time and his denial?

The basic principle concerning cosmetic surgeries is prohibition, except in cases of medical treatment or to remove a defect or disfigurement. Whoever performs such a surgery without a legitimate necessity has committed a sin and must repent. If the first surgery was to correct a crookedness or remove a defect, then it is permissible. However, the second surgery, which altered the shape of the nose without a legitimate justification, is forbidden.

Nevertheless, since the questioner did not intend to alter Allah's creation, this removes the blame from him. He only needs to seek Allah's forgiveness for his negligence in not stopping the doctor or replacing him.

As for the doctor, he can be sued because he performed the second surgery without explicit permission from the questioner, and he is considered liable for what occurred.