Respiratory sound analysis is a crucial tool for screening asthma and other pulmonary pathologies, yet traditional auscultation remains subjective and experience-dependent. Our prior research established a CNN baseline using DenseNet201, which demonstrated high sensitivity in classifying respiratory sounds. In this work, we (i) adapt the Audio Spectrogram Transformer (AST) for respiratory sound analysis and (ii) evaluate a multimodal Vision-Language Model (VLM) that integrates spectrograms with structured patient metadata. AST is initialized from publicly available weights and fine-tuned on a medical dataset containing hundreds of recordings per diagnosis. The VLM experiment uses a compact Moondream-type model that processes spectrogram images alongside a structured text prompt (sex, age, recording site) to output a JSON-formatted diagnosis. Results indicate that AST achieves approximately 97% accuracy with an F1-score around 97% and ROC AUC of 0.98 for asthma detection, significantly outperforming both the internal CNN baseline and typical external benchmarks. The VLM reaches 86-87% accuracy, performing comparably to the CNN baseline while demonstrating the capability to integrate clinical context into the inference process. These results confirm the effectiveness of self-attention for acoustic screening and highlight the potential of multimodal architectures for holistic diagnostic tools.