Do I have to buy the full CC or is there a way to buy After Effects ONLY at a student price?

Hi erik.d.nilsson,

I'm moving this discussion to the Student and Teacher Edition Information forum in case you have further questions about student pricing.

Student CC is basically $20 per month which is the same as an individual app plan. You can get a single app, but if you want AE and Premiere Pro it's going to cost you almost as much as getting the entire suite.

Unless you are just going to create very short sequences or effects shots you'll need a NLE like Premiere Pro. To take advantage of things like Character Animator you'll need Illustrator or Photoshop. AE as a stand alone is pretty limiting. While it's a great app for visual effects and motion graphics it's just lousy at editing video and even worse at trying to do anything with sound. If your computer will run the latest versions of the software you'll be a lot better off with the entire suite.

If you go to the Adobe main site and check the purchase options you'll find a chat button. They will be able to guide you through a student purchase:

Adobe Customer Service Chat Window