In the evolving energy landscape where prosumers play an increasingly important role, establishing of an efficient data exchange architecture is essential for building a resilient and secure energy infrastructure. This paper introduces the Privacy-Sensitive Distributed Optimization (PSDO) framework, a decentralized management scheme designed to prioritize privacy safeguards in prosumer-driven systems. The primary objective of the PSDO approach is to empower prosumers, allowing them to autonomously manage their energy needs through decentralized decision-making. To achieve this goal, the PSDO framework combines decentralized optimization techniques with differential privacy. This integration serves a dual purpose: preserving prosumers' control over their energy management and ensuring privacy of their sensitive information. By leveraging decentralized optimization, the PSDO framework enables prosumers to maximize the benefits derived from decentralized systems, promoting improved autonomy in energy management. Simultaneously, prosumers' sensitive data is safeguarded through the implementation of differential privacy measures. Through extensive experiments on the IEEE 33-bus radial distribution system, the PSDO algorithm demonstrated its adeptness in converging to the optimal solution while rigorously upholding differential privacy.