Detecting testimonial injustice is an essential element of addressing inequities and promoting inclusive healthcare practices, many of which are life-critical. However, using a single demographic factor to detect testimonial injustice does not fully encompass the nuanced identities that contribute to a patient's experience. Further, some injustices may only be evident when examining the nuances that arise through the lens of intersectionality. Ignoring such injustices can result in poor quality of care or life-endangering events. Thus, considering intersectionality could result in more accurate classifications and just decisions. To illustrate this, we use real-world medical data to determine whether medical records exhibit words that could lead to testimonial injustice, employ fairness metrics (e.g. demographic parity, differential intersectional fairness, and subgroup fairness) to assess the severity to which subgroups are experiencing testimonial injustice, and analyze how the intersectionality of demographic features (e.g. gender and race) make a difference in uncovering testimonial injustice. From our analysis, we found that with intersectionality we can better see disparities in how subgroups are treated and there are differences in how someone is treated based on the intersection of their demographic attributes. This has not been previously studied in clinical records, nor has it been proven through empirical study.