You've got an English test tomorrow, right? Then you shouldn't be wasting time on math homework tonight.
Literal
Tomorrow [topic-は] English [possessive-の] test [probably-だろう], then tonight [topic-は] math [possessive-の] homework [to-に] get-bogged-down [must-not-ちゃだめだ].
かかずらわっちゃだめだ is colloquial — かかずらう ('to be occupied with, to get bogged down in') + ちゃ (contracted ては) + だめだ ('no good'). The sentence pairs a だろう confirmation question with a prohibition, creating a natural scolding or advice pattern.