In the field of medical diagnosis, how to identify medical condition efficiently and give an accurate diagnosis on the edge is crucial for patient treatment. The memristor-based analog content-addressable memory (ACAM) emerges as a highly parallel accelerator for template matching technology. This study proposes a novel timing complementary 2T1R ACAM design for multimodal medical diagnosis that significantly reduces operational energy and area. The simulation results show that such design could achieve 2 ns matching speed and 34.2 fJ energy consumption per unit, while simultaneously reducing the area by 33% compared to the state-of-the-art design. Besides, a multimodal medical diagnosis task is demonstrated on a simulated ACAM array with a suitable configuration of design parameters.