Kate, you asked for a reference request as a high school student interested in getting started in computational science, which I think I can tackle fairly specifically. As long as you are comfortable (or getting comfortable) with Calculus, I think there are two great self-interest textbooks for you to go, depending on your interest and access to Python and MATLAB.
The first book, A Primer on Scientific Programming, by Hans Petter Langtangen, requires no more background than "high school mathematics" and some Calculus. It is not free, but there may be a copy of the book at your local college library. Python and all of the tools associated with the book are freely available and can be downloaded online.
The second book, Experiments with MATLAB, by Cleve Moler, "is an electronic book with chapters that supplement high school and early college courses in mathematics and technical computing, including calculus and matrix theory. The expected background includes algebra, trigonometry, and some familiarity with computers." Here, the situation is the opposite. The book itself is free but a student version of MATLAB (if it is not available in your local high school or college computer laboratory) will cost you $100 for a license.
If you do not have access to MATLAB, there is also the free (open source) GNU Octave. The core numerical commands (especially in the context you are interested in) are completely compatible with MATLAB (i.e., you can use most MATLAB scripts without any modification), although graphical capabilities may differ.
Let me be the third moderator to welcome you to the community and encourage you to ask good questions here, as well as helping when you have knowledge to provide.
Hans Petter and Cleve are two of the world's most recognized experts in computational science. They both have very clear writing styles, and I strongly recommend either of these books.