With the current advancement in the Internet, there has been a growing demand for building intelligent and smart systems that can efficiently address the detection of health-related problems on social media, such as the detection of depression and anxiety. These types of systems, which are mainly dependent on machine learning techniques, must be able to deal with obtaining the semantic and syntactic meaning of texts posted by users on social media. The data generated by users on social media contains unstructured and unpredictable content. Several systems based on machine learning and social media platforms have recently been introduced to identify health-related problems. However, the text representation and deep learning techniques employed provide only limited information and knowledge about the different texts posted by users. This is owing to a lack of long-term dependencies between each word in the entire text and a lack of proper exploitation of recent deep learning schemes. In this paper, we propose a novel framework to efficiently and effectively identify depression and anxiety-related posts while maintaining the contextual and semantic meaning of the words used in the whole corpus when applying bidirectional encoder representations from transformers (BERT). In addition, we propose a knowledge distillation technique, which is a recent technique for transferring knowledge from a large pretrained model (BERT) to a smaller model to boost performance and accuracy. We also devised our own data collection framework from Reddit and Twitter, which are the most common social media sites. Finally, we employed word2vec and BERT with Bi-LSTM to effectively analyze and detect depression and anxiety signs from social media posts. Our system surpasses other state-of-the-art methods and achieves an accuracy of 98% using the knowledge distillation technique.