This study explores public perception of public hospitals in the Ecuadorian province of Manabí through sentiment analysis applied to social media comments (X, Reddit, Facebook) posted between 2017 and 2024, including the context of the COVID-19 pandemic. We implemented an LSTM network, known for capturing contextual dependencies in natural language, instead of using traditional approaches. This choice represents a novel methodological contribution in real-world health domains in Spanish. The model achieved outstanding metrics, with F1 Scores of 0.93 (negative) and 0.90 (positive), and an overall accuracy close to 90%. The temporal and institution-based analysis revealed a notable heterogeneity in the distribution of sentiments and a growing evolution in the linguistic complexity of the comments since 2018. These findings provide actionable insights for service improvement, underscoring the potential of deep NLP as a key tool for quality management in public health.