Social media platforms, such as Twitter, provide a suitable avenue for users (people or patients) concerned on health questions to discuss and share information with each other. In December 2019, a few coronavirus disease cases were first reported in China. Soon after, the World Health Organization (WHO) declared a state of emergency due to the rapid spread of the virus in other parts of the world. In this work, we used automated extraction of COVID-19 discussion from Twitter and a natural language processing (NLP) method based on topic modeling to discover the main questions related to COVID-19 from tweets. Moreover, we created a Named Entity Recognition (NER) model to identify the main entities of four different categories: disease, drug, person, and organization. Our findings can help policy makers and health care organizations to understand the issues of people on COVID-19 and it can be used to address them appropriately.