In recent years, there has been a dramatic progress in the photonics field of disordered media, ranging from applications in solar collectors, photocatalyzers, random lasing, and other novel photonic devices, to investigations into fundamental topics, such as localization of light and other phenomena involving photon interactions. Anderson localization of light is an open researcher frontier, which has greatly attracted the attention of researchers in the past few decades. In this work, we study the transport of light in a strongly disordered optical medium composed by core-shell nanoparticles (TiO2@Silica) suspended in ethanol solution. We demonstrate the crossover from a diffusive transport to a localization transition regime as TiO2@Silica nanoparticle concentration is increased. A striking phenomenon of enhanced absorption, mainly near the input border, arises at the localization transition, from which an increase of refractive index was inferred. An increase of the density of localized states and absorption near the input border is reported when the incidence angle is increased. The specular reflection, measured for the photons that enter the sample, is considerably lower than the effective internal reflection undergone by the coherently backscattered photons in the exact opposite direction, indicating a nonreciprocal propagation of light (parity-symmetry breaking). A theoretical simulation, performed through random-matrix theory, agrees satisfactorily with the experimental results, showing the generality of this approach to address transport phenomena.