Radiology reports are one of the main forms of communication between radiologists and other clinicians, and contain important information for patient care. In order to use this information for research and automated patient care programs, it is necessary to convert the raw text into structured data suitable for analysis. State-of-the-art natural language processing (NLP) domain-specific contextual word embeddings have been shown to achieve impressive accuracy for these tasks in medicine, but have yet to be utilized for section structure segmentation. In this work, we pre-trained a contextual embedding BERT model using breast radiology reports and developed a classifier that incorporated the embedding with auxiliary global textual features in order to perform section segmentation. This model achieved 98% accuracy in segregating free-text reports, sentence by sentence, into sections of information outlined in the Breast Imaging Reporting and Data System (BI-RADS) lexicon, which is a significant improvement over the classic BERT model without auxiliary information. We then evaluated whether using section segmentation improved the downstream extraction of clinically relevant information such as modality/procedure, previous cancer, menopausal status, purpose of exam, breast density, and breast MRI background parenchymal enhancement. Using the BERT model pre-trained on breast radiology reports, combined with section segmentation, resulted in an overall accuracy of 95.9% in the field extraction tasks. This is a 17% improvement, compared to an overall accuracy of 78.9% for field extraction with models using classic BERT embeddings and not using section segmentation. Our work shows the strength of using BERT in the analysis of radiology reports and the advantages of section segmentation by identifying the key features of patient factors recorded in breast radiology reports.