Mild dry cough for 21+ days : Coronoa?

Hi Dr, I came to my hometown from Chennai 19 days back and I'm self quartining myself in a room from then. My mild cough started while was in Chennai two days before I planned to leave to my hometown. So, I'm yet to test for covid-19. Does my mild cough warrants a covid-19 test? I am also scared to go to a Government hospital to get it tested as there is a chance to get exposed to the virus there. I just spoke to a Health Inspector to my area and he is happy to write a consultation for me to take covid-19 test in hospital tomorrow. But I'm really confused , whether, 1) Is it good to get tested just bcoz I hav mild cough for 21+ days and also came to my hometown just from Chennai? 2) Or should I stay home instead of getting tested as therr is a chance of exposure when I go to testing center. I'm really confused..pls advise me I don't have other symptoms other than cough