Integrating distributed energy resources (DERs) is a critical step toward addressing the global climate crisis. This transformation has driven the transition from traditional consumers to prosumers and given rise to new energy sharing business models. Existing works have extensively studied prosumer energy sharing mechanisms, yet little attention has been paid to privacy protection, particularly when communication constraints are taken into account. In this paper, we study an energy sharing mechanism where information is exchanged over wireless channels via over-the-air (OTA) multiple-input multiple-output (MIMO) aggregation to exploit spectral efficiency for scalable prosumer coordination. To characterize the privacy leakage risk during data transmission process, we introduce an adversarial attack model and demonstrate that, under certain conditions, the platform can extract and recover prosumers' private parameters from the base station observations. To safeguard the energy sharing mechanism against such attacks, we propose a differentially private equilibrium-seeking algorithm, analyze the achievable privacy level, and establish convergence guarantees that quantify the impact of privacy on the convergence accuracy. Numerical experiments demonstrate that our approach effectively protects prosumers' privacy while converging to near-optimal solutions.