Social media is recognized as an important source for deriving insights into public opinion dynamics and social impacts due to the vast textual data generated daily and the 'unconstrained' behavior of people interacting on these platforms. However, such analyses prove challenging due to the semantic shift phenomenon, where word meanings evolve over time. This paper proposes an unsupervised dynamic word embedding method to capture longitudinal semantic shifts in social media data without predefined anchor words. The method leverages word co-occurrence statistics and dynamic updating to adapt embeddings over time, addressing the challenges of data sparseness, imbalanced distributions, and synergistic semantic effects. Evaluated on a large COVID-19 Twitter dataset, the method reveals semantic evolution patterns of vaccine- and symptom-related entities across different pandemic stages, and their potential correlations with real-world statistics. Our key contributions include the dynamic embedding technique, empirical analysis of COVID-19 semantic shifts, and discussions on enhancing semantic shift modeling for computational social science research. This study enables capturing longitudinal semantic dynamics on social media to understand public discourse and collective phenomena.