The drug development pipeline for a new compound can last 10-20 years and cost over $10 billion. Drug repurposing offers a more time- and cost-effective alternative. Computational approaches based on network graph representations, comprising a mixture of disease nodes and their interactions, have recently yielded new drug repurposing hypotheses, including suitable candidates for COVID-19. However, these interactomes remain aggregate by design and often lack disease specificity. This dilution of information may affect the relevance of drug node embeddings to a particular disease, the resulting drug-disease and drug-drug similarity scores, and therefore our ability to identify new targets or drug synergies. To address this problem, we propose constructing and learning disease-specific hypergraphs in which hyperedges encode biological pathways of various lengths. We use a modified node2vec algorithm to generate pathway embeddings. We evaluate our hypergraph's ability to find repurposing targets for an incurable but prevalent disease, Alzheimer's disease (AD), and compare our ranked-ordered recommendations to those derived from a state-of-the-art knowledge graph, the multiscale interactome. Using our method, we successfully identified 7 promising repurposing candidates for AD that were ranked as unlikely repurposing targets by the multiscale interactome but for which the existing literature provides supporting evidence. Additionally, our drug repositioning suggestions are accompanied by explanations, eliciting plausible biological pathways. In the future, we plan on scaling our proposed method to 800+ diseases, combining single-disease hypergraphs into multi-disease hypergraphs to account for subpopulations with risk factors or encode a given patient's comorbidities to formulate personalized repurposing recommendations.Supplementary materials and code: https://github.com/ayujain04/psb_supplement.