The COVID-19 pandemic - as a massive disruption - has significantly increased the need for medical services putting an unprecedented strain on health systems. This study presents a robust location-allocation model under uncertainty to increase the resiliency of health systems by applying alternative resources, such as backup and field hospitals and student nurses. A multi-objective optimization model is developed to minimize the system's costs and maximize the satisfaction rate among medical staff and COVID-19 patients. A robust approach is provided to face the data uncertainty, and a new mathematical model is extended to linearize a nonlinear constraint. The ICU beds, ward beds, ventilators, and nurses are considered the four main capacity limitations of hospitals for admitting different types of COVID-19 patients. The sensitivity analysis is performed on a real-world case study to investigate the applicability of the proposed model. The results demonstrate the contribution of student nurses and backup and field hospitals in treating COVID-19 patients and provide more flexible decisions with lower risks in the system by managing the fluctuations in both the number of patients and available nurses. The results showed that a reduction in the number of available nurses incurs higher costs for the system and lower satisfaction among patients and nurses. Moreover, the backup and field hospitals and the medical staff elevated the system's resiliency. By allocating backup hospitals to COVID-19 patients, only 37% of severe patients were lost, and this rate fell to less than 5% after establishing field hospitals. Moreover, medical students and field hospitals curbed the costs and increased the satisfaction rate of nurses by 75%. Finally, the system was protected from failure by increasing the conservatism level. With a 2% growth in the price of robustness, the system saved 13%.