Understanding emotions that people express during large-scale crises helps inform policy makers and first responders about the emotional states of the population as well as provide emotional support to those who need such support. We present CovidEmo, a dataset of ~3,000 English tweets labeled with emotions and temporally distributed across 18 months. Our analyses reveal the emotional toll caused by COVID-19, and changes of the social narrative and associated emotions over time. Motivated by the time-sensitive nature of crises and the cost of large-scale annotation efforts, we examine how well large pre-trained language models generalize across domains and timeline in the task of perceived emotion prediction in the context of COVID-19. Our analyses suggest that cross-domain information transfers occur, yet there are still significant gaps. We propose semi-supervised learning as a way to bridge this gap, obtaining significantly better performance using unlabeled data from the target domain.