Prehospital emergency healthcare personnel are responsible for finding, rescuing, and taking prehospital care of emergency patients. They are regularly exposed to stressful and traumatic lifesaving situations. The stress involved can impact their performance and can cause mental disorders in the long term. Stress inoculation training (SIT) inoculates individuals to potential stressors by letting them practice stress-coping skills in a controlled environment. Our work explores a story-driven stressful virtual environment design that can potentially be used for SIT in the new context of emergency healthcare personnel. Users role-play a first-time emergency worker on a rescue mission. The interactive storytelling is designed to engage users and elicit strong emotional responses, and follows the three-act structure commonly found in films and video games. To understand the stress-inducing and sense of presence qualities of our approach including the previously untested impact of an emotional connection factor, we conduct a between-subjects experiment involving 60 subjects. Results show that the approach successfully induces stress by increasing heart rate, galvanic skin response, and subjective stress rating. Questionnaire results indicate positive presence. One subject group engages in an initial friendly conversation with a virtual co-worker to establish an emotional connection. Another group includes no such conversation. The group with the emotional connection shows higher physiological stress levels and more occurrences of subject behaviors reflecting presence. Medical experts review our approach and suggest several applications that can benefit from its stress inducing ability.