This work proposes a band-switchable electrically small antenna (ESA) system for a wearable health monitoring device. The system operates at multiple 5G-NR bands (875–934 MHz and 1.72–2.2 GHz) using a switchable configuration. The antenna consists of multi-resonant shorted strips that have been miniaturized to fit in meandered form into an area of 63.2$\times$25 mm$^2$ (0.19$\times$0.08$\lambda^2$) available in the intended health monitoring device. To enable operation at two distinct modes, the antenna feedline has been integrated with a switch, which is then matched using lumped matching components. Results indicate that the ESA system operates at 875–900 MHz in Configuration 1, and at 898–934 MHz and at 1.72–2.2 GHz in Configuration 2. The device has been fabricated and integrated into a compact 3D printed casing prior to experimental evaluations. In addition to studying the switchable reflection and radiation performance, the ESA is also evaluated in the presence of a human body phantom. Simulated specific absorption rate levels are less than 0.47 W/kg averaged over 1 g of tissue, which complies with international standards.