The photon is a quantum mechanical point particle/entity in the table of the standard model of physics. Point means that its four vector is a function of (x,y,z,t) , it has no volume in space. It is one of the founding elements of the theory .
Question: If we shoot a single photon will that single photon at a certain position of the propagation axis be the excitation of both E and M fields, (and so the photon itself would have two fields coupled) or is it just the excitation for one of them and then 'changes' to being the excitation of the other one as it propagates?
In quantum mehanics, the point elementary particles are described by solutions of the corresponding quantum mechanical equations, Dirac for fermions, klein Gordon for bosons and a form of quantized maxwell's equation for photons.
One usually does not discuss the wave function of a photon because the classical description of light emerges smoothly from the quantum mechanical (it does need the mathematics of quantum field theory to understand the link) and is very accurate and much more easy to use, then going to individual photon levels.
The classical electric and magnetic fields of the electromagnetic radiation are built up by a confluence of the wave functions of the zillions of photons that build it up. The fields exist in the wavefunction of the photon, i.e. before it is squared to give the probability of finding the photon with energy h*nu and an (x,y,z,t) point. It is the superposed wavefunctions that will build in confluence the classical light wave with its E and B fields.
A single photon, when detected (interacting with another particle) will only enter with the complex conjugate squared of the wave function, so the information of the electric and magnetic field is irrelevant other than its effect on the probability of the interaction happening.