The highest photon energy ever measured and transplanckian energies What is the highest energy of we have measured of a photon by any physical experiment? 
Has a transplanckian energy photon been measured? Can we study them -if they exist- with special relativity?
 A: Cosmic rays have the highest energy particles that have ever been detected. An upper limit has been deduced for the energy of photons:

From direct observations of the longitudinal development of ultra-high energy air showers performed with the Pierre Auger Observatory, upper limits of 3.8%, 2.4%, 3.5% and 11.7% (at 95% c.l.) are obtained on the fraction of cosmic-ray photons above 2, 3, 5 and 10 EeV View the MathML source(1EeV≡10^18eV), respectively. These are the first experimental limits on ultra-high energy photons at energies below 10 EeV. The results complement previous constraints on top–down models from array data and they reduce systematic uncertainties in the interpretation of shower data in terms of primary flux, nuclear composition and proton-air cross-section.

The LHC delivers TeVs (10^12eV) so that limits the  maximum laboratory energies possible for photons.
Transplanckian is not an everyday word in physics,is used by cosmologists:

The basic idea is that we do not know what happens at higher energies, or shorter wavelengths, than Λ,and that we therefore are forced to encode our ignorance in terms of initial conditions when the modes enter into the regime that we understand. The unknown high energy physics is usually referred to as transplanckian, and the hope is that, e.g., string theory eventually will give us the means to derive these effective initial conditions.

You ask:

Has a transplanckian energy photon been measured?

The universe at present is over thirteen billion years away from the inflation period implied by the definition of the term.  So the answer is no.

Can we study them -if they exist- with special relativity

Any studies can only be done using cosmological models which project at the beginning of the Big Bang. This gives an order of magnitude of the energy fluctuations that such back projections estimate from the cosmic microwave backround: One needs general relativity too, to create these models, and not only.

These spectral distortions depend on the shape and amplitude of the primordial power spectrum at wavenumbers k < 10^4 Mpc^{-1}. Here we study constraints on the primordial power spectrum derived from COBE/FIRAS and forecasted for PIXIE. 

