WAV File (Audio) Sped Up When Imported into After Effects

The actual key to this is simple, go to windows at the top, select preview, then select the frame rate preview type that matches the audio best. No doubt it's 23.9 something, so choose 24. Then press play and the preview speed should sound fine....

I had a similar problem - found that if my COMP was at 24 frames a minute and playback was 29.97 I had that problem.
Fixed by changing comp or playback framerate.

p.s. appreciate @Rick Gerard's tip on creating markers in Audition - Thanks Rick!

Make sure your audio file is 16 bit 48 kHz PCM Wave or AIFF. Create a new composition using one of the Comp Presets like the HD 1080P 29.97 preset. Drag your audio file into the composition. Make sure the info Panel is visible and the Preview Panel has been expanded, Preview the audio. After the Comp has cached the Info Panel should show you that the comp is playing in real-time. Previews may run faster than real-time when the preview is rendering, but they should slow down as long as you have not mucked up the preview settings. If it still does not work try resetting your preferences.

If that is not the case we need the system, OS, comp, source footage, and workflow details. A screenshot showing what you are doing to the layers (press uu) would also help. Cropped screenshots are almost completely useless. 

By the way, the easiest way to animate to audio is to open up the track in Audition, all beat or work markers, label them, then save the WAV file and return to AE. You'll find the markers on the audio track and that makes the work go a lot faster. 

You should also consider breaking up the song into phrases or sections that are no longer than 4 or 8 bars. Animate each section as a separate comp, then render them and put the whole thing back in Premiere Pro and do your final edit there. It sounds like more work, but the project will take less time, changes will be easier, and the likelihood of a busted render goes down exponentially.