Is the grade I received considered Haram, and would intentionally compensating for this mistake in the future with a similar mistake in another exam make the final grade not a result of cheating?

You are not required to intentionally make a mistake in another exam, and there is no harm in correcting the error that the teacher pointed out to you because he did not ask you to, and you corrected it from your own knowledge. If an error occurred, it is on the teacher, not on you. Ibn Uthaymin permitted a student to write an answer he heard from others if it came to him without intending to cheat, considering it a provision from Allah.