The capabilities of Large Language Models (LLMs) have advanced since their popularization a few years ago. The healthcare sector operates on, and generates a large volume of data annually and thus, there is a growing focus on the applications of LLMs within this sector. There are a few medicine-oriented evaluation datasets and benchmarks for assessing the performance of various LLMs in clinical scenarios; however, there is a paucity of information on the real-world usefulness of LLMs in context-specific scenarios in resourceconstrained settings. In this study, 16 iterations of a decision support tool for medical emergencies using 4 distinct generalized LLMs were constructed, alongside a combination of 4 Prompt Engineering techniques: In-Context Learning with 5-shot prompting (5SP), chain-of-thought prompting (CoT), self-questioning prompting (SQP), and a stacking of self-questioning prompting and chain-of-thought (SQCT). In total 428 model responses were quantitatively and qualitatively evaluated by 22 clinicians familiar with the medical scenarios and background contexts. Our study highlights the benefits of In-Context Learning with few-shot prompting, and the utility of the relatively novel self-questioning prompting technique. We also demonstrate the benefits of combining various prompting techniques to elicit the best performance of LLMs in providing contextually applicable health information. We also highlight the need for continuous human expert verification in the development and deployment of LLM-based health applications, especially in use cases where context is paramount.