Understanding protein function and developing molecular therapies require deciphering the cell types in which proteins act as well as the interactions between proteins. However, modeling protein interactions across diverse biological contexts, such as tissues and cell types, remains a significant challenge for existing algorithms. We introduce Pinnacle, a flexible geometric deep learning approach that is trained on contextualized protein interaction networks to generate context-aware protein representations. Leveraging a human multi-organ single-cell transcriptomic atlas, Pinnacle provides 394,760 protein representations split across 156 cell type contexts from 24 tissues and organs. Pinnacle's contextualized representations of proteins reflect cellular and tissue organization and Pinnacle's tissue representations enable zero-shot retrieval of the tissue hierarchy. Pretrained Pinnacle's protein representations can be adapted for downstream tasks: to enhance 3D structure-based protein representations for important protein interactions in immuno-oncology (PD-1/PD-L1 and B7-1/CTLA-4) and to study the effects of drugs across cell type contexts. Pinnacle outperforms state-of-the-art, yet context-free, models in nominating therapeutic targets for rheumatoid arthritis and inflammatory bowel diseases, and can pinpoint cell type contexts that predict therapeutic targets better than context-free models (29 out of 156 cell types in rheumatoid arthritis; 13 out of 152 cell types in inflammatory bowel diseases). Pinnacle is a graph-based contextual AI model that dynamically adjusts its outputs based on biological contexts in which it operates.