We present a full quantum model to study the fidelity of single photons with different quantum states propagating in a medium exhibiting electromagnetically induced transparency (EIT). By using the general reservoir theory, we can calculate the quantum state of the transmitted probe photons that reveal the EIT phenomenon predicted by semiclassical theory while reflecting the influence of the quantum fluctuations of the strong coupling field. Our study shows that the coupling field fluctuations not only change the quantum state of the probe photons, but also slightly affect its transmittance. Moreover, we demonstrate that the squeezed coupling field can enhance the influence of its fluctuations on the quantum state of the probe photons, which means that the EIT effect can be manipulated by controlling the quantum state properties of the coupling field. The full quantum theory in this paper is suitable for studying quantum systems related to the EIT mechanism that would allow us to examine various quantum effects in EIT-based systems from a full quantum perspective.