A string of te-form verbs chaining actions: 酔って + はじけて + 晴らす. はじける (literally 'to burst / pop') is used figuratively for 'to let loose / cut loose / go wild.' 鬱憤を晴らす is a set collocation for 'to vent / clear pent-up frustration,' where 晴らす '(to) clear away' is used for dispelling negative emotions. ~たほうがいいんじゃないか is the rhetorical-question advice frame 'wouldn't it be better to X?'