This paper focuses on modeling gender-based and pair-or-group disparities in online supportive interactions among adolescents. To address the limitations of conventional social science methods in handling large datasets, this research employs language models to detect supportive interactions based on the Social Support Behavioral Code and to model their distribution. The study conceptualizes detection as a classification task, constructs a new dataset, and trains predictive models. The novel dataset comprises 196,772 utterances from 2165 users collected from Instant Messenger apps. The results show that the predictions of language models can be used to effectively model the distribution of supportive interactions in private online dialogues. As a result, this study provides new computational evidence that supports the theory that supportive interactions are more prevalent in online female-to-female conversations. The findings advance our understanding of supportive interactions in adolescent communication and present methods to automate the analysis of large datasets, opening new research avenues in computational social science.