As of early 2019, the COVID-19 outbreak has ensued in millions of deaths, making it one of the worst pandemics in history. In addition to wearing masks, increasing sanitation, and avoiding crowds, widespread vaccination is crucial for preventing virus transmission. Despite significant progress in vaccine research and policy implementations, widespread immunization remains challenging. Analysis of exchanges on social media regarding COVID-19 vaccines has revealed significant uncertainty and mistrust in vaccines. As a result, ongoing evaluation of trust and confidence in COVID-19 vaccines is critical to crafting successful communication approaches for promoting extensive vaccination. This study aims to use content analysis of tweets about COVID-19 vaccines while also examining the user accounts generating them to provide evidence of fluctuations in public views toward COVID-19 vaccines. The proposed framework collects and processes data from social media networks, particularly Twitter, before presenting various analytics based on the different analyses performed through machine learning and deep learning algorithms. We hypothesize that a qualitative study starting from the pandemic would identify themes in public discourses (particularly those with negative sentiment or evidence of misleading information) that circulated during the developmental and mass release phases of COVID-19 vaccines. Therefore, it could inform and aid healthcare officials, public health agencies, and policymakers in increasing awareness and educational interventions for COVID-19 vaccines.