Mental illness among Bangladeshi students at universities is getting more severe due to academic stress, economic hardship, social stigma, and limited access to culturally specific psychological services. With this need gap in mind, this paper introduces BanglaMind, an AI-powered mental health chatbot designed to recognize emotional distress, suicidal ideation, and user intent from Bangla-language conversation while generating empathetic and ethical real-time responses. A 2,480-sized custom Bangla text data was prepared, consisting of actual and synthetically generated data, and annotated with emotion, sentiment, intent, and suicide risk tags. Different models including Logistic Regression, Random Forest, Multinomial Naive Bayes, and Bangla-BERT were trained and tested against TF-IDF, Word2Vec, and transformer-based embeddings. Among them, Bangla-BERT achieved the highest performance with 97.38% accuracy and improved F1-score and contextual understanding for all classification tasks, while Random Forest was suitable for real-time use due to its computational complexity. The chatbot system was developed using the MERN stack with an interactive anonymous web interface possessing real-time Bangla typing, emotional tagging, suicide risk alert, and integrated mental health resources. As opposed to previous research focused on sentiment or depression analysis in isolation, BanglaMind presents a complete and ethically sound solution by integrating multi-label classification with an end-to-end conversational interface. This work is a critical breakthrough in Bangla NLP and South Asian mental health technology by closing the gap between emotion-sensitive AI and culturally aware, low-resource mental health care systems in South Asia.