Antiphotons will never exist. Or they always have. An antiparticle is just the same particle with the opposite charge on it - a negative charge instead of a positive, or vice versa. Photons (as well as gluons and a few other force-carriers) are electrically neutral. And I'm sure we can agree that -0 is the same as +0, so an antiphoton is the same thing as a photon.

"splitting a proton or a neutron" - it's not quite as simple as that, as quarks cannot exist on their own, but that's perhaps a chat for another day...