The increasing popularity of online social networks (OSNs) attracted growing interest in modeling social interactions. On online social platforms, a few individuals, commonly referred to as influencers, produce the majority of content consumed by users and hegemonize the landscape of the social debate. However, classical opinion models do not capture this communication asymmetry. We develop an opinion model inspired by observations on social media platforms {with two main objectives: first, to describe this inherent communication asymmetry in OSNs, and second, to model the effects of content personalization. We derive a Fokker-Planck equation for the temporal evolution of users' opinion distribution and analytically characterize the stationary system behavior. Analytical results, confirmed by Monte-Carlo simulations, show how strict forms of content personalization tend to radicalize user opinion, leading to the emergence of echo chambers, and favor structurally advantaged influencers. As an example application, we apply our model to Facebook data during the Italian government crisis in the summer of 2019. Our work provides a flexible framework to evaluate the impact of content personalization on the opinion formation process, focusing on the interaction between influential individuals and regular users. This framework is interesting in the context of marketing and advertising, misinformation spreading, politics and activism.