Been in contact with someone who tested positive for corona on thursday 16/7/20,i developed a bad dry cough on friday,i can't take deep breaths,triggers 'coughing fit', best way to describe, is that lungs feels 'tight', do i need to be get tested?

Yes: In order to come to a firm opinion who should have a proper evaluation which can be done via telemedicine. Based on what I read alone it seems like you should be tested for COVID 19 .

See below: Covid-19: https://www.cdc.gov/coronavirus/2019-ncov/index.html Please contact your doctor by phone for further evaluation and mechanism for testing in your area. Wear a mask, stay away from others, practice hand hygiene. If you develop breathing difficulty, go to the nearest hospital, immediately. Wish you good health.