Acute asthma risk assessment requires rapid interpretation of respiratory sounds, oxygenation, airflow limitation, speech ability, work of breathing, mental status, and response to reliever therapy. Conventional audio-only classifiers can detect wheeze-like patterns but often lack transparent clinical reasoning and safe escalation logic. This paper presents AeroSpectra Sentinel, a client-side research prototype and decision-support workflow that combines short-time Fourier transform (STFT) respiratory sound analysis, lightweight machine-learning screening, clinical feature fusion, and a five-stage large language model (LLM) prompt-chaining process. The workflow separates signal acquisition, preprocessing, acoustic feature extraction, ML screening, clinical guardrails, and FHIR-ready reporting. We evaluated the audio screening component on a public respiratory sound dataset containing 1,211 WAV recordings from five labels. Using a stratified subset of 584 recordings, a random forest achieved 91.10% binary accuracy and 78.69% F1-score for asthma-vs-non-asthma screening, while a feature-based multilayer perceptron achieved 89.73% accuracy and 78.26% F1-score. A compact log-spectrogram CNN achieved 73.29% accuracy and 55.17% F1-score. Multiclass classification achieved 77.40% accuracy and 77.23% macro-F1. To evaluate the LLM workflow, we conducted a scenario-based audit on 40 simulated clinical vignettes comparing one-shot prompting, prompt chaining, prompt chaining with guardrails, and prompt chaining with guardrails plus FHIR schema validation. The guardrail-plus-schema variant achieved the strongest simulated safety and documentation consistency. AeroSpectra Sentinel is intended as a research prototype, not as a diagnostic medical device or clinically validated risk-assessment product.