Large Language Models (LLMs) are increasingly adopted across domains such as education, healthcare, and finance. In healthcare, LLMs support tasks including disease diagnosis, abnormality classification, and clinical decision-making. Among these, multi-abnormality classification of radiology reports is critical for clinical workflow automation and biomedical research. Leveraging strong natural language processing capabilities, LLMs enable efficient processing of unstructured medical text and reduce the administrative burden of manual report analysis. To improve performance, LLMs are often fine-tuned on private, institution-specific datasets such as radiology reports. However, this raises significant privacy concerns: LLMs may memorize training data and become vulnerable to data extraction attacks, while sharing fine-tuned models risks exposing sensitive patient information. Despite growing interest in LLMs for medical text classification, privacy-preserving fine-tuning for multi-abnormality classification remains underexplored. To address this gap, we propose a differentially private (DP) fine-tuning framework for multi-abnormality classification from free-text radiology reports. Our approach integrates differential privacy with Low-Rank Adaptation (LoRA) to efficiently fine-tune LLMs on sensitive clinical data while mitigating leakage risks. We further employ labels generated by a larger LLM to train smaller models, enabling efficient inference under strong privacy guarantees. Experiments on MIMIC-CXR and CT-RATE demonstrate the effectiveness of our DP-LoRA framework across varying privacy regimes. On MIMIC-CXR, our method achieves weighted F1-scores up to 0.89 under moderate privacy budgets, approaching non-private LoRA (0.90) and full fine-tuning (0.96), confirming that strong privacy can be achieved with only modest performance trade-offs.