The COVID-19 pandemic has severely affected people's daily lives and caused tremendous economic loss worldwide. However, its influence on people's mental health conditions has not received as much attention. To study this subject, we choose social media as our main data resource and create by far the largest English Twitter depression dataset containing 2,575 distinct identified depression users with their past tweets. To examine the effect of depression on people's Twitter language, we train three transformer-based depression classification models on the dataset, evaluate their performance with progressively increased training sizes, and compare the model's "tweet chunk"-level and user-level performances. Furthermore, inspired by psychological studies, we create a fusion classifier that combines deep learning model scores with psychological text features and users' demographic information and investigate these features' relations to depression signals. Finally, we demonstrate our model's capability of monitoring both group-level and population-level depression trends by presenting two of its applications during the COVID-19 pandemic. We hope this study can raise awareness among researchers and the general public of COVID-19's impact on people's mental health.