Hallucinations in medical large language models (LLMs) pose serious risks for clinical decision support, particularly when models must reason over complex electronic health records (EHRs). However, existing benchmarks often lack a realistic clinical context and provide limited insight into how hallucinations can be mitigated in practice. We introduce Med-HEAL, a framework for systematically identifying, analyzing, and mitigating hallucinations in medical LLMs using clinically grounded data. Building on the EHRNoteQA benchmark derived from MIMIC-IV discharge summaries, we construct a hallucination dataset by evaluating BioMistral-7B on open-ended clinical question answering tasks. Model outputs are labeled through a dual evaluation pipeline that combines LLM-as-a-Judge assessment (GPT-4o) with human auditing by medical student reviewers, producing correctness judgments and annotations of reasoning errors via a custom web-based evaluation system. We then leverage this dataset to investigate mitigation strategies: a self-critique pipeline, in which the test model reviews its own answers to detect potential errors and regenerates responses for flagged cases, and retrieval-augmented in-context learning (RA-ICL), which exposes the model to hallucinated and corrected examples. Experiments across five open-source LLMs-BioMistral, Llama-3.1, DeepSeek, Qwen2.5, and Qwen3, show that the self-critique strategy improves accuracy for three of five models (p < 0.05) without requiring parameter updates. Med-HEAL provides both a reusable hallucination dataset and a practical framework for studying and mitigating hallucinations in medical LLMs, supporting safer deployment of AI systems in clinical environments. Our code and data are publicly available at https://github.com/yimingliao-blad/med-heal.git.