although the file size is incredibly huge, you may Try some presets from Adobe Media Encoder :
Composition > Add to Adobe Media Encoder
You are not understanding how AE fundamentally works and that is causing your frustration.
AE does not simply make changes to existing footage. AE is not a basic video editor (although, those don't technically do that either).
AE is a complex compositing, visual effects, and motion graphics application.
AE works internally with completely uncompressed data. That means, when you import your highly compressed file (which is only 15 GB), AE decompresses it and works with full frame information. So, the size it is when you import it is completely irrelevant to the size the output file is going to be.
When you choose your output and render settings, that and that alone is what determines the size of your file. The default render settings in After Effects is to output a completely uncompressed file. That's fine for an intermediate (although, I would recommend using Cineform or DNxHD codecs in AE's render queue for intermediate files since they're much smaller, but still high quality). Anyway, you can take the intermediate file into Adobe Media Encoder to make your deliverable OR you can send your AE comp directly to AME to make your deliverable.
You probably want to choose the MP4 option and a decent data rate that will get you close to your original file size. But that's all very dependent on what you are planning to do with this video you're making and what you've done to it.
Are you still facing this problem? If not, let us know how you solved it. If so, please let us know so we can assist you further.