The phrases "What is my offense" and "What is my sin" mean basically the same thing. [Jacob](rc://en/tw/dict/bible/names/jacob) is asking [Laban](rc://en/tw/dict/bible/names/laban) to tell him what he did wrong. AT: "What have I done wrong that you should pursue me like this?" (See: [[rc://en/ta/man/translate/figs-parallelism]])
Here the word "hotly" means [Laban](rc://en/tw/dict/bible/names/laban) urgently chased [Jacob](rc://en/tw/dict/bible/names/jacob) intending to capture him. (See: [[rc://en/ta/man/translate/figs-idiom]])