The two words that mean "punishing someone who hurt you" are Vengeance and avenge. The world Vengeance comes from the latin word vindicare which means to inflict punhishment for a past injury. The world avenge has origins in old french evolving from the latin vindicare which means to inflict harm in return. Both of this worlds mean to return harm or punish those who wrong/harmed you.
The two words that have meanings similar to "punishing someone who hurt you" are human vengeance. The word vengence carries the meaning of causing any kind of harm or retribution to someone who has harmed you or a person close to you.
A similar meaning could be found in avenge the wrong, though it is a three-word expression.
