Along with the Coronavirus pandemic, another crisis has manifested itself in the form of mass fear and panic phenomena, fuelled by incomplete and often inaccurate information. There is therefore a tremendous need to address and better understand COVID-19's informational crisis and gauge public sentiment, so that appropriate messaging and policy decisions can be implemented. In this research article, we identify public sentiment associated with the pandemic using Coronavirus specific Tweets and R statistical software, along with its sentiment analysis packages. We demonstrate insights into the progress of fear-sentiment over time as COVID-19 approached peak levels in the United States, using descriptive textual analytics supported by necessary textual data visualizations. Furthermore, we provide a methodological overview of two essential machine learning classification methods, in the context of textual analytics, and compare their effectiveness in classifying Coronavirus Tweets of varying lengths. We observe a strong classification accuracy of 91% for short Tweets, with the Naive Bayes method. We also observe that the logistic regression classification method provides a reasonable accuracy of 74% with shorter Tweets, and both methods showed relatively weaker performance for longer Tweets. This research provides insights into Coronavirus fear sentiment progression, and outlines associated methods, implications, limitations and opportunities.