In recent years, due to an increase in nuclear families, there has been a sudden shift in social norms, such as single child, small gatherings, overuse of the internet, etc. This new normal is leading to growing stress, anxiety and loneliness in the young adults. This research primarily focuses on university students facing mental-health challenges driven by academic stress, social isolation, and digital overload. To address this growing concern, this research presents an agentic solution, BlumyAI. This is an agent-based counsellor who would act as a first-level solution to a high number of patients. This agentic solution would assist the limited number of available professionals in addressing the scarcity of psychiatrists in a university. BlumyAI adopts a modular multi-agent framework for proactive mental health counselling by integrating empathetic dialogue, psychometric profiling, and a decision to escalate to a professional counsellor. Specifically, BlumyAI implements three layers: an Interaction Layer for multi-turn dialogue; a Cognitive Layer for patient profiling; and an Escalation Layer, which implements Whittle-index Restless Multi-Armed Bandit policies for optimal counsellor allocation. Towards the end, BlumyAI is evaluated using both real-world and synthetic mental-health datasets. From the experimental results, BlumyAI outperforms other baselines, such as Large Language Models, RAG, and rule-based, by 8-15%, in terms of accuracy, empathy alignment, and safety calibration metrics. Also, BlumyAI is validated by psychiatrists, who confirmed over 85% clinical agreement in terms of risk, emotion, action, and empathy dimensions. In this regard, BlumyAI presents a safe, interpretable, clinically sound and scalable framework for digitally assisting student mental-health support and early intervention.