I've never heard that one, but it might be a regional variant. I always heard the other one.
Sticks and stones may break my bones but words will hurt forever.
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]