With the development of 5G networks, traditional communication systems face increasing challenges in meeting high bandwidth and low latency requirements. The integration of edge computing and semantic communication helps alleviate these issues, yet challenges remain in resource allocation, model updating, and privacy protection. Moreover, existing semantic communication models often fail to capture hierarchical features, and their robustness under dynamic channel conditions remains limited. To address these problems, this paper proposes a distributed semantic communication network (DSCN) framework that reduces data redundancy, improves computational efficiency, safeguards privacy, and optimizes resource allocation. In this framework, we propose a new federated learning (FL) aggregation scheme called federated multi-center parameter sharing (FedMcs) to improve model training efficiency and system fault tolerance. Additionally, for image semantic communication, this paper proposes an adaptive channel conditions and transmission rates joint source-channel coding (ACRJSCC) framework based on the Swin Transformer, together with a dual adaptive module (ACRM) to improve global modeling and adaptability in dynamic environments. Experimental results show that the proposed schemes outperform other schemes, particularly in image reconstruction tasks.