Multi-access edge computing (MEC) has attracted the interest of the research and industrial community to support Internet of things (IoT) applications by enabling efficient data processing and minimizing latency. This paper presents significant contributions toward optimizing the resource allocation and enhancing the decision-making process in edge computing environments. Specifically, the TRUST-ME model is introduced, which consists of multiple edge servers and IoT devices, i.e., users, with varied computing tasks offloaded to the MEC servers. A utility function was designed to quantify the benefits in terms of latency and cost for the IoT device while utilizing the MEC servers’ computing capacities. The core innovation of our work is a novel trust model that was designed to evaluate the IoT devices’ confidence in MEC servers. This model integrates both direct and indirect trust and reflects the trustworthiness of the servers based on the direct interactions and social feedback from other devices using the same servers. This dual trust approach helps with accurately gauging the reliability of MEC services and ensuring more informed decision making. A reinforcement learning framework based on the optimistic Q-learning with an upper confidence bounds action selection algorithm enables the IoT devices to autonomously select a MEC server to process their computing tasks. Also, a multilateral bargaining model is proposed for fair resource allocation of the MEC servers’ computing resources to the users while accounting for their computing demands. Numerical simulations demonstrated the operational effectiveness, convergence, and scalability of the TRUST-ME model, which was validated through real-world scenarios and comprehensive comparative evaluations against existing approaches.