Semantic communication is a new paradigm that aims at providing more efficient communication for the next-generation wireless network. It focuses on transmitting extracted, meaningful information instead of the raw data. However, deep learning-enabled image semantic communication models often require a significant amount of time and energy for training, which is unacceptable, especially for mobile devices. To solve this challenge, our paper first introduces a distributed image semantic communication system where the base station and local devices will collaboratively train the models for uplink communication. Furthermore, we formulate a joint optimization problem to balance time and energy consumption on the local devices during training while ensuring effective model performance. An adaptable resource allocation algorithm is proposed to meet requirements under different scenarios, and its time complexity, solution quality, and convergence are thoroughly analyzed. Experimental results demonstrate the superiority of our algorithm in resource allocation optimization against existing benchmarks and discuss its impact on the performance of image semantic communication systems.