As mobile healthcare applications increasingly rely on cloud-based systems, ensuring data security while maintaining sustainability remains a critical challenge. Traditional centralized architectures often struggle with latency, energy inefficiency, and single points of failure, especially when handling sensitive medical data. This paper introduces a novel architecture for secure and sustainable mobile healthcare data management in cloud environments. By integrating Federated Learning, Blockchain, and Function-as-a-Service (FaaS), we address the limitations of traditional centralized architectures that struggle with security, latency, and energy efficiency. Our approach leverages FL to decentralize model training on mobile devices, minimizing data transmission and reducing energy consumption. Blockchain technology provides an immutable and decentralized audit trail, ensuring data integrity and preventing tampering. FaaS dynamically allocates computational resources, further optimizing energy efficiency and scalability. Simulations demonstrate significant reductions in energy costs and enhanced data protection compared to traditional methods. This work offers a practical and scalable solution for secure and sustainable mobile healthcare data management, addressing the growing demands of healthcare cloud services.