I'm not a native speaker, so almost every time I hear that phrase it ends after "sticks and stones", because on TV and movies, that's usually enough for the intended audience.

After Googling, I think I might have picked up this version from Tim Minchins song "prejudice" [1] although Google also come up with this clip where a senator also use the "break my heart" version, clearly when it was meant for him to say "never harm" [2]

1: https://www.youtube.com/watch?v=KVN_0qvuhhw

2: https://youtu.be/QoMheenRUHM?t=92