And it was an accident because you only meant to get rid of the threat. Would you go to the dungeons?
It would depend on local laws, and those would be determined by the king or lord. There were no constitutions in those times, so anything the king wanted, the king got. If the father was a friend of the king, you'd probably be punished worse. If he was an enemy of the king, you might receive an honor. Do some research.
But this sounds like the very premiss upon which your story could be structured. There are uncounted mitigating circumstances that could/would/should alter the outcome. Are you the elder brother, heir to your father's fortune and name? Have you a younger brother who knows it was all an accident, none of it your fault, yet despises you for being born first, thus leaving him penniless save what your graces cast in his direction? Might he not spin a different story that surely casts you into the gloom and filth and him into the glory of inheritance? I think the question is not if you would go to the dungeon, but what story could you tell that takes you there and back, or saves you from it.
That's a marvelous idea; my character does have a lot of anger issues. That could escalate it even further and make him more interesting.
Well, my point in writing that was to show you that it doesn't matter in the slightest what the law would have said according to the premiss you provided. What matters is what you want to have happen and then write the story that makes that happen. If you want him to end up in the dungeon, there are a million and one paths to take him there. If you don't want him to land there, the same holds holds true. So my question is, do you want him in the dungeon or not? If the answer is yes or if it's no, then the most important question, the real question, is why? Why is the most important question because the answer to why determines the motivation for the story, the underlying emotive force that moves it forward.
you are the creator of this world and these people, so you can make it be ok, or a crime, as you feel works best for the plot...