Computer Science is about writing software in the way that Astronomy is about telescopes.
Another way to put it is that Computer Science is a Mathematics field that is about the study of computation. You can do significant amounts of computation without a computer, and you can study pretty much every topic about computation with nothing more than a pencil and paper.
Programming is simply a convenient way to use these great devices we have to assist us in better understanding computation, and a good CS program will go very deep in how modern computers work, what they can and cannot compute, and so on. You'll likely have changes to study computational complexity, queuing theory, grammars and regular languages, and so on.
For all this you need a really strong foundation in mathematics. For an undergrad, you should be able to handle just about anything in single and multi-variate Calculus, Linear Algebra, Discrete Mathematics, and be able to build proofs and if you really want to push as an undergrad more advanced classes. If you can't hang with this coursework, you can't do CS.
It's okay, you might be better suited to a Software Engineering degree or and Information Systems degree where programming and engineering practices are favored. To be honest, these degrees are far more practical for the regular old software developer than is CS. Most programming jobs aren't trying to invent an algorithm, or determine the runtime efficiency of some system.