Personalized Federated Learning (pFL) can improve the accuracy of local models and provide enhanced edge intelligence without exposing the raw data in Mobile Edge Computing (MEC). However, in the MEC environment with constrained communication resources, transmitting the entire model between the server and the clients in traditional pFL methods imposes substantial communication overhead, which can lead to inaccurate personalization and degraded performance of mobile clients. In response, we propose a Communication-Efficient pFL architecture to enhance the performance of personalized models while minimizing communication overhead in MEC. First, a Knowledge-Aware Parameter Coaching method (KAPC) is presented to produce a more accurate personalized model by utilizing the layer-wise parameters of other clients with adaptive aggregation weights. Then, convergence analysis of the proposed KAPC is developed in both the convex and non-convex settings. Second, a Bidirectional Layer Selection algorithm (BLS) based on self-relationship and generalization error is proposed to select the most informative layers for transmission, which reduces communication costs. Extensive experiments are conducted, and the results demonstrate that the proposed KAPC achieves superior accuracy compared to the state-of-the-art baselines, while the proposed BLS substantially improves resource utilization without sacrificing performance.