'publish-{custom-post-type}' hook is firing many, many times on a single submit

I’m writing my first plugin, and I have a the following action that’s added (within a class) when the plugin is loaded:

add_action( 'publish_appt', array($this, 'save_my_appt_metadata'),10,3);

function save_my_appt_metadata($post_id, $post, $update = true)
    {
        //do some stuff, then
        $this->create_my_appt($post_id, $post);
    }
function create_my_appt($post_id, $post) {
       //create a google calendar event
    }

When I publish my ‘appt’ custom post type, the save_my_appt and create_my_appt functions are run infinitely until a fatal time-out error occurs. This results in something like 60 or 80 calendar entries! What am I overlooking here?