サマリー
It’s a contraction of じゃなければ if I remember correctly, together with a negative like the だめ that follows it, it’s a way of expressing “must” (“if I don’t do X, it’s no good” is just a roundabout way of saying “I must do X” 
). I think the sentence would mean something as “it has to be to that extent”, or in normal English we would say something like “I have to at least do that”.
サマリー
I think you got the translation mostly right I interpreted the 自分 more as “myself”, so it refers to Nishikata himself. The への is simply a combination of the particles へ and の, the combination basically states that the へ here applies to the word that follows it instead of the verb in the sentence, so 自分への罰 is simply “a punishment to me” or “a punishment for me”. I ended up reading the entire sentence as “this is a punishment for me for always getting teased to much”, although the more literal translation would be “this is a punishment for the me who always gets teased too much”, but that sounds a bit odd in English