To choose the appropriate resources for their healthcare needs (e.g., primary care (GP) or emergency department (ED)), patients seeking acute care must self-triage based on their own assessment of their symptoms and severity. However, as patients typically lack sufficient medical knowledge, self-triage decisions can often be inaccurate. In response, healthcare and technology companies have been developing and deploying virtual triage tools designed to help patients make better and more efficient self-triage decisions. However, the operational implications of such tools have not yet been assessed. This paper therefore develops a queueing game model to investigate the impact of virtual triage in the acute care setting and policies to maximize its efficacy. We find that, due to its decentralized nature, when virtual triage excessively recommends emergency (primary) care, it could bring about a decrease in ED (GP) visits. Another important finding is that for any arbitrary patient self-triage accuracy, the adoption of informative virtual triage can worsen system performance, even when the virtual triage recommendation is reasonably accurate. To unlock the potential operational benefits of virtual triage, we characterize the optimal virtual triage accuracy subjective to the receiver operating characteristic (ROC) curve. We then investigate how the optimal accuracy changes when patient composition and acute care cost parameters change and as the triage capability of the tool improves.