Content-based medical image retrieval is an important diagnostic tool that improves the explainability of computer-aided diagnosis systems and provides decision making support to healthcare professionals. Medical imaging data, such as radiology images, are often multimorbidity; a single sample may have more than one pathology present. As such, image retrieval systems for the medical domain must be designed for the multi-label scenario. In this paper, we propose a novel multi-label metric learning method that can be used for both classification and content-based image retrieval. In this way, our model is able to support diagnosis by predicting the presence of diseases and provide evidence for these predictions by returning samples with similar pathological content to the user. In practice, the retrieved images may also be accompanied by pathology reports, further assisting in the diagnostic process. Our method leverages proxy feature vectors, enabling the efficient learning of a robust feature space in which the distance between feature vectors can be used as a measure of the similarity of those samples. Unlike existing proxy-based methods, training samples are able to assign to multiple proxies that span multiple class labels. This multi-label proxy assignment results in a feature space that encodes the complex relationships between diseases present in medical imaging data. Our method outperforms state-of-the-art image retrieval systems and a set of baseline approaches. We demonstrate the efficacy of our approach to both classification and content-based image retrieval on two multimorbidity radiology datasets.