The rapid evolution of mobile edge computing (MEC) has introduced significant challenges in optimizing resource allocation in highly dynamic wireless communication systems, in which task offloading decisions should be made in real-time. However, existing resource allocation strategies cannot well adapt to the dynamic and heterogeneous characteristics of MEC systems, since they are short of scalability, context-awareness, and interpretability. To address these issues, this paper proposes a novel retrieval-augmented generation (RAG) method to improve the performance of MEC systems. Specifically, a latency minimization problem is first proposed to jointly optimize the data offloading ratio, transmit power allocation, and computing resource allocation. Then, an LLM-enabled information-retrieval mechanism is proposed to solve the problem efficiently. Extensive experiments across multi-user, multi-task, and highly dynamic offloading scenarios show that the proposed method consistently reduces latency compared to several DL-based approaches, achieving 57% improvement under varying user computing ability, 86% with different servers, 30% under distinct transmit powers, and 42% for varying data volumes. These results show the effectiveness of LLM-driven solutions to solve the resource allocation problems in MEC systems.