Help! Exported file distorted the audio [after effects]

The difference between digital audio and analog audio is that when audio levels go over 0db they are gone. There is nothing higher. It doesn't matter if the audio is 8, 16, or 32 bit. There is nothing above 0. When you push levels past that you may still hear something on your speakers or headphones, but when it is rendered, all of the nuances are gone and you have a mess. 

Pressing LL to reveal the Audio Spectrum will tell you if you have levels that are clipped. If they are clipped in the original and you bring the levels down, they are still clipped. After Effects has only the most basic audio tools. The tools in Premiere Pro are a little better, but if you want to seriously manipulate audio you need Audition or a similar audio app. Then you need to look at all the parameters. I would not attempt to do what you are describing in any other Adobe app. Open the audio file in Audition and work in it there paying careful attention to every monitoring tool you can look at. It's the only way to get anything close to professional results with the kind of EQ you are describing. When the original file is perfect you can fiddle a bit with the audio section of the Render Queue or the Media Encoder, but most of the time, and especially if you are going to share on social media, YouTube or Vimeo or any other streaming services, you should use the presets that follow their guidelines. Sending out-of-spec files to any streaming services will not let their compression software do the best job possible with your files. You might as well try compressing the file with a sledgehammer. 

The specifics will depend. There certainly may be a way to just pull down a few frequencies while not reducing the overall volume too much, but without any reference of how it looks on your end and what settings you use nobody can advise specifically. You may simply be seeing some unsavory combination of AE's very limited audio processing causing some unwanted resampling and messing up your sound regardless of that Bristol style/ Ambient Dub thing being bass-heavy to begin with.

Mylenium

Impossible to know much without any info on actual render settings, how the waveform looks in AE and so on. The only thing that's for sure is that the bass is massively oversaturated in the source file already and short of some heavy massaging with a parametric equalizer and perhaps some conventional tweaks in a graphical equalizer there may be no way to get it to render correctly. At the very least the mastering volume would have to be taken down to prevent the blurting, which is a simple feedback artifact. The speaker can't respond quickly enough to the frequencies being pumped into it and amplitutes multiply/ add. Physics, you know. You would simulate it using some delay and boost on the specific frequencies.

Mylenium