In modern terminology, mass means invariant mass. See Why is there a controversy on whether mass increases with speed? . The mass of a photon is zero. So to make this question more intelligible based on modern usage, a better title would be "Greatest energy possible for a single photon."
I have been told that photons can not be blue shifted to the point where they become black holes
This is true because the criterion for being a black hole (light can't escape to infinity) is observer-independent. It doesn't mean that there's a limit on how much of a blueshift you can have. There is no such limit. Although it is true for a collapsing star, in its rest frame, that $r/m \lesssim G/c^2$ is a criterion for being a black hole, this is not true in other frames of reference. It would make sense in terms of Newtonian mechanics if the criterion was $r/m \lesssim G/c^2$, but general relativity is different because in GR the source of gravity isn't mass, it's the stress-energy tensor.
Also, by extension, how short a wavelength could it have.
We don't have a theory of quantum gravity, so we don't know for sure how to interpret the Planck length. However, it probably shouldn't be interpreted as a minimum length scale. That would violate Lorentz invariance.
If the wavelength gets to the Plank scale does it become a particle, or matter?
A photon is both a wave and a particle regardless of its wavelength. Modern physicists don't really use the term "matter" much, but to the extent that they do, they mean fermions. A photon is a boson regardless of its wavelength.