To shut out sounds, the thing that seems to work for me is to play thunderstorm sounds. Because it's got a high degree of randomness across the frequency spectrum, and its spectrum varies over short timescales, external noise is masked even if it's still audible - because the brain can easily fit it into the thunderstorm pattern. Whereas if I'm annoyed by something, my brain will pick it out from behind music in listening to, even if it's quieter.

When I'm hearing someone else's thump thump music and my ear buds aren't sufficient to block it, that's the only thing I've found to work.