As far as I know all energy is associated with some sort of mass, whether that be rest mass or some other type of mass such as relativistic mass. But as I am not well educated on this, I could very easily be completely wrong.
This is wrong. Photons have no rest mass, and it is misleading to insist that it has a "relativistic mass". Look at the expression for relativistic mass. It requires the existence of a non-zero rest mass!
One should also stop using "relativistic mass".