Will I have committed the sin of breaking an oath after swearing to harm whoever harmed me, and is it permissible to swear by Allah to harm a Muslim?

You have acted correctly and been successful in forgiving and accepting reconciliation. By doing so, you will receive a great reward, as Allah Almighty says: "and those who restrain anger and pardon people" and "So whoever pardons and makes reconciliation - his reward is due from Allah." Furthermore, forgiveness increases a servant in honor. There is no sin upon you for breaking your oath here; rather, it is preferable because reconciliation is better, and you must offer expiation for breaking an oath.