Rapid discovery of new diseases, such as COVID-19 can enable a timely epidemic response, preventing the large-scale spread and protecting public health. However, limited research efforts have been taken on this problem. In this paper, we propose a contrastive learning-based modeling approach for COVID-19 coughing and breathing pattern discovery from non-COVID coughs. To validate our models, extensive experiments have been conducted using four large audio datasets and one image dataset. We further explore the effects of different factors, such as domain relevance and augmentation order on the pre-trained models. Our results show that the proposed model can effectively distinguish COVID-19 coughing and breathing from unlabeled data and labeled non-COVID coughs with an accuracy of up to 0.81 and 0.86, respectively. Findings from this work will guide future research to detect an outbreak of a new disease early.