Most people I know go get tested in that situation. In my case I would get tested if I knew I had been in a high risk situation. Otherwise I would lay low until specific symptoms develop such as fever, weakness, cough and loss of smell and taste.
Of all the symptoms they list for Covid-19 (not just the main ones like shortness of breath, inability to smell or taste things, and coughing), surprisingly sneezing and runny nose are not on the lists very often. I think at this time of year sneezing and runny nose alone are more likely to be allergies.
Testing. There is testing for each which revels which it is. We shouldn't guess at it. :>)