As the air molecules are environment for carrying sound waves, could stream of photons be environment for carrying electromagnetic waves? What contradictions cause this assumption in the existing theories?
Your analogy does not hold because air molecules are a medium on which sound is an effect. Sound is not built up from air molecules.
Photons are not a medium which when "vibrated" displays electromagnetic waves.
Photons are the basic building blocks of classical electromagnetic waves, they are the quantum manifestation of the electromagnetic forces in the microcosm of elementary particles. A photon is one of the elementary particles in the standard model which describes all data of particle physics.
A very large number of photons, as in a beam of light, builds up the electromagnetic waves that we observe in classical distances, which are the solutions of the classical Maxwell's equations. An exposition of how the quantum framework develops into the classical waves s can be found here.
Here is the disproof of your hypothesis.
Consider a magnet inside a perfectly dark room. The magnetic field due to this magnet will still be there inside the room even though there is no photons. Now disturb this magnet (say by spinning it around an axis). Maxwell's equations tells you that when there is nothing else, any disturbance in the electromagnetic field will propagate in the form of a electromagnetic wave. So we have an electromagnetic wave in our dark room where photons are absent.