Relational Agents' (RAs) ability to maintain socio-emotional relationships with users can be an asset to COVID-19 patients. The goal of this research was to identify principles for designing an RA that can act as a health professional for a COVID-19 patient. We first identified tasks that such an RA can provide by interviewing 33 individuals, who had recovered from COVID-19. The transcribed interviews were analyzed using qualitative thematic analysis. Based on the findings, four sets of hypothetical conversations were handcrafted to illustrate how the proposed RA will execute the identified tasks. These conversations were then evaluated by 43 healthcare professionals in a qualitative study. Thematic analysis was again used to identify characteristics that would be suitable for the proposed RA. The results suggest that the RA must: model clinical protocols; incorporate evidence-based interventions; inform, educate, and remind patients; build trusting relationships, and support their socio-emotional needs. The findings have implications for designing RAs for other healthcare contexts beyond the pandemic.