In spanish questions intonation changes occur only on the last word(s), not the whole sentence. I’m not a linguistic, but I think it’s so you can be sure a sentence is a question from the start.
That might be the case in the dialect you’re familiar with, but “¿Me dijiste que no te moleste?” has a different intonation to “Me dijiste que no te moleste.” in my Spanish (starting from “dijiste”).
As for English, questions normally start either with a question word or a (auxiliary) verb, while affirmations normally start with the subject. See “You told me not to bother you.” vs. “Did you tell me not to bother you?”. Using just intonation is possible (“You told me not to bother you?!??”), but when in writing, it’s usually formatted in a way that highlights it because it usually indicates outrage/disbelief.