The rapid spread of COVID-19 cases in recent months has strained hospital resources, making rapid and accurate triage of patients presenting to emergency departments a necessity. Machine learning techniques using clinical data such as chest X-rays have been used to predict which patients are most at risk of deterioration. We consider the task of predicting two types of patient deterioration based on chest X-rays: adverse event deterioration (i.e., transfer to the intensive care unit, intubation, or mortality) and increased oxygen requirements beyond 6 L per day. Due to the relative scarcity of COVID-19 patient data, existing solutions leverage supervised pretraining on related non-COVID images, but this is limited by the differences between the pretraining data and the target COVID-19 patient data. In this paper, we use self-supervised learning based on the momentum contrast (MoCo) method in the pretraining phase to learn more general image representations to use for downstream tasks. We present three results. The first is deterioration prediction from a single image, where our model achieves an area under receiver operating characteristic curve (AUC) of 0.742 for predicting an adverse event within 96 hours (compared to 0.703 with supervised pretraining) and an AUC of 0.765 for predicting oxygen requirements greater than 6 L a day at 24 hours (compared to 0.749 with supervised pretraining). We then propose a new transformer-based architecture that can process sequences of multiple images for prediction and show that this model can achieve an improved AUC of 0.786 for predicting an adverse event at 96 hours and an AUC of 0.848 for predicting mortalities at 96 hours. A small pilot clinical study suggested that the prediction accuracy of our model is comparable to that of experienced radiologists analyzing the same information.