Compiling Python 3 extension module on Mac

I'm trying to write a Python extension module in C. I'm running macOS Catalina and have a Homebrew installation of Python 3 (with default installation settings). When I try to compile the following file:

#include <Python/Python.h>

static PyObject* world(PyObject* self, PyObject* args)
{
    printf("Hello world!\n");
    Py_RETURN_NONE;
}

static PyMethodDef methods[] = {
    {"world", world, METH_VARARGS, "Prints \"Hello world!\""},
    {NULL, NULL, 0, NULL}
};

static struct PyModuleDef module = {
    PyModuleDef_HEAD_INIT,
    "name for the module",
    "docstring for the module",
    -1,
    methods
};

PyMODINIT_FUNC PyInit_hello(void)
{
    return PyModule_Create(&module);
}

by running gcc hello.c in my terminal, I get the following messages:

hello.c:15:5: error: use of undeclared identifier
      'PyModuleDef_HEAD_INIT'
    PyModuleDef_HEAD_INIT,
    ^
hello.c:14:27: error: variable has incomplete type
      'struct PyModuleDef'
static struct PyModuleDef module = {
                          ^
hello.c:14:15: note: forward declaration of 'struct PyModuleDef'
static struct PyModuleDef module = {
              ^
hello.c:24:12: warning: implicit declaration of function
      'PyModule_Create' is invalid in C99
      [-Wimplicit-function-declaration]
    return PyModule_Create(&module);
           ^
1 warning and 2 errors generated.

Is there a way to fix this? I've tried playing around with the -L and -I flags to no avail. I think this might be happening because it’s using the header for Python 2 rather than Python 3.