The demands of the modern world are increasingly responsible for causing psychological burdens and bringing adverse impacts on our mental health. As a result, neural conversational agents with empathetic responding and distress management capabilities have recently gained popularity. However, existing end-to-end empathetic conversational agents often generate generic and repetitive empathetic statements such as "I am sorry to hear that", which fail to convey specificity to a given situation. Due to the lack of controllability in such models, they also impose the risk of generating toxic responses. Chatbots leveraging reasoning over knowledge graphs is seen as an efficient and fail-safe solution over end-to-end models. However, such resources are limited in the context of emotional distress. To address this, we introduce HEAL, a knowledge graph developed based on 1M distress narratives and their corresponding consoling responses curated from Reddit. It consists of 22K nodes identifying different types of stressors, speaker expectations, responses, and feedback types associated with distress dialogues and forms 104K connections between different types of nodes. Each node is associated with one of 41 affective states. Statistical and visual analysis conducted on HEAL reveals emotional dynamics between speakers and listeners in distress-oriented conversations and identifies useful response patterns leading to emotional relief. Automatic and human evaluation experiments show that HEAL's responses are more diverse, empathetic, and reliable compared to the baselines.