Detecting human stress levels and emotional states with physiological body-worn sensors is a complex task, but one with many health-related benefits. Robustness to sensor measurement noise and energy efficiency of low-power devices remain key challenges in stress detection. We propose SELFCARE, a fully wrist-based method for stress detection that employs context-aware selective sensor fusion that dynamically adapts based on data from the sensors. Our method uses motion to determine the context of the system and learns to adjust the fused sensors accordingly, improving performance while maintaining energy efficiency. SELF-CARE obtains state-of-the-art performance across the publicly available WESAD dataset, achieving 86.34% and 94.12% accuracy for the 3-class and 2-class classification problems, respectively. Evaluation on real hardware shows that our approach achieves up to 2.2x (3-class) and 2.7x (2-class) energy efficiency compared to traditional sensor fusion.