Mental disorders including depression, anxiety, and other neurological disorders pose a significant global challenge, particularly among individuals exhibiting social avoidance tendencies. This study proposes a hybrid approach by leveraging smartphone sensor data measuring daily physical activities and analyzing their social media (Twitter) interactions for evaluating an individual's depression level. Using CNN-based deep learning models and Naive Bayes classification, we identify human physical activities accurately and also classify the user sentiments. A total of 33 participants were recruited for data acquisition, and nine relevant features were extracted from the physical activities and analyzed with their weekly depression scores, evaluated using the Geriatric Depression Scale (GDS) questionnaire. Of the nine features, six are derived from physical activities, achieving an activity recognition accuracy of 95%, while three features stem from sentiment analysis of Twitter activities, yielding a sentiment analysis accuracy of 95.6%. Notably, several physical activity features exhibited significant correlations with the severity of depression symptoms. For classifying the depression severity, a support vector machine (SVM)-based algorithm is employed that demonstrated a very high accuracy of 94%, outperforming alternative models, e.g., the multilayer perceptron (MLP) and k-nearest neighbor. It is a simple approach yet highly effective in the long run for monitoring depression without breaching personal privacy.