I have Python on my Ubuntu system, but gcc can't find Python.h

I am on a school computer, so I can't install anything. I am trying to create C code which can be run in Python. It seems all the articles I am finding on it require you to use #include <Python.h> I do this, but when I compile it complains that *there is no such file or directory.* The computer has Python (at least it has the `python` command in the terminal, and we can run whatever Python code we want). I typed in `locate Python.h` in the terminal, but it found nothing. I have two questions: 1. Can I write C code that I can call in Python without `Python.h`? 2. Am I missing something, and the computer actually has `Python.h`?