A novel distributed algorithm is proposed in this paper for a network of consumers coupled by energy resource sharing constraints, which aims at minimizing the aggregated electricity costs. Each consumers is equipped with an energy management system that schedules the shiftable loads accounting for user preferences, while an aggregator entity coordinates the consumers demand and manages the interaction with the grid and the shared energy storage system (ESS) via a distributed strategy. The proposed distributed coordination algorithm requires the computation of Mixed Integer Linear Programs (MILPs) at each iteration. The proposed approach guarantees constraints satisfaction, cooperation among consumers, and fairness in the use of the shared resources among consumers. The strategy requires limited message exchange between each consumer and the aggregator, and no messaging among the consumers, which protects consumers privacy. Performance of the proposed distributed algorithm in comparison with a centralized one is illustrated using numerical experiments.