I am looking for a way to make audio sound like it's above your head and then below your head in Audacity. Is there a way to accomplish this?
Like Mark mentions, you should have a look at Ambisonics and/or Binaural (HRTF) sound. Additionally, you could also have a look at techniques like VBAP (Vector Base Amplitude Panning) and DirAC (Directional Audio Coding), which are meant to be used for multichannel reproduction, but they could also be used for speaker emulation in binaural rendering. For more info on those techniques you could start with:
Finally, please keep in mind that Audacity is just a tool and it won't necessarily provide a solution to all your problems. As long as you understand the underlying principles and phenomena of your problem you may be able to use Audacity (or any other Editor or DAW) to achieve what you intend to do.