In addressing the challenges of heterogeneous data and limited communication resources in wireless networks, which often hinder the performance of federated learning, this article introduces a personalized learning approach. This approach not only addresses data heterogeneity but also optimizes resource management in wireless networks. We construct an optimization model aimed at maximizing the decay of the global loss function in a single iteration. The problem is divided into two subproblems: 1) allocation of device-local fine-tuning learning rates and 2) communication resources, tackled through an iterative method. The solutions involve determining near-optimal fine-tuning learning rates and optimizing device resource block and transmission power allocation. Our simulation results demonstrate that, under the constraints of wireless network resources and data heterogeneity, our algorithm outperforms baseline methods in terms of convergence speed and accuracy in personalized federated learning.