Mental health diseases affect children's lives and well-beings which have received increased attention since the COVID-19 pandemic. Analyzing psychiatric clinical notes with topic models is critical to evaluate children's mental status over time. However, few topic models are built for longitudinal settings, and they fail to keep consistent topics and capture temporal trajectories for each document. To address these challenges, we develop a longitudinal topic model with time-invariant topics and individualized temporal dependencies on the evolving document metadata. Our model preserves the semantic meaning of discovered topics over time and incorporates heterogeneity among documents. In particular, when documents can be categorized, we propose an unsupervised topics learning approach to maximize topic heterogeneity across different document groups. We also present an efficient variational optimization procedure adapted for the multistage longitudinal setting. In this case study, we apply our method to the psychiatric clinical notes from a large tertiary pediatric hospital in Southern California and achieve a 38% increase in the overall coherence of extracted topics. Our real data analysis reveals that children tend to express more negative emotions during state shutdowns and more positive when schools reopen. Furthermore, it suggests that sexual and gender minority (SGM) children display more pronounced reactions to major COVID-19 events and a greater sensitivity to vaccine-related news than non-SGM children. This study examines the progression of children's mental health during the pandemic and offers clinicians valuable insights to recognize the disparities in children's mental health related to their sexual and gender identities.