The COVID-19 pandemic has imposed additional stress on population health that may result in a change of sleeping behavior. In this study, we hypothesized that using natural language processing to explore social media would help with assessing the mental health conditions of people experiencing insomnia after the outbreak of COVID-19. We designed a retrospective study that used public social media content from Twitter. We categorized insomnia-related tweets based on time, using the following two intervals: the prepandemic (January 1, 2019, to January 1, 2020) and peripandemic (January 1, 2020, to January 1, 2021) intervals. We performed a sentiment analysis by using pretrained transformers in conjunction with Dempster-Shafer theory (DST) to classify the polarity of emotions as positive, negative, and neutral. We validated the proposed pipeline on 300 annotated tweets. Additionally, we performed a temporal analysis to examine the effect of time on Twitter users' insomnia experiences, using logistic regression. We extracted 305,321 tweets containing the word insomnia (prepandemic tweets: n=139,561; peripandemic tweets: n=165,760). The best combination of pretrained transformers (combined via DST) yielded 84% accuracy. By using this pipeline, we found that the odds of posting negative tweets (odds ratio [OR] 1.39, 95% CI 1.37-1.41; P<.001) were higher in the peripandemic interval compared to those in the prepandemic interval. The likelihood of posting negative tweets after midnight was 21% higher than that before midnight (OR 1.21, 95% CI 1.19-1.23; P<.001). In the prepandemic interval, while the odds of posting negative tweets were 2% higher after midnight compared to those before midnight (OR 1.02, 95% CI 1.00-1.07; P=.008), they were 43% higher (OR 1.43, 95% CI 1.40-1.46; P<.001) in the peripandemic interval. The proposed novel sentiment analysis pipeline, which combines pretrained transformers via DST, is capable of classifying the emotions and sentiments of insomnia-related tweets. Twitter users shared more negative tweets about insomnia in the peripandemic interval than in the prepandemic interval. Future studies using a natural language processing framework could assess tweets about other types of psychological distress, habit changes, weight gain resulting from inactivity, and the effect of viral infection on sleep.