I worry seeing those queues of people waiting for a walk-in test. If they don't have Covid-19 then standing for several hours (even outside) with people who may well have Covid-19 is only going to increase a person's risk of catching it.
Anyway, if you have the variant of Covid-19 that comes with a cough, it going to be pretty bad. or at least the shortness of breath will be bad.
If you don't have a Covid-19 cough, you might have a temperature or have lost your sense of smell/taste.
If your only symptom is a mild cough, it doesn't seem necessary to queue up to get a test, especially if there aren't enough.
Cough is not the only symptom of Covid-19 and is very pronounced in those for whom it is the main symptom.
If you only have a mild occasional cough, you are probably likely to be Covid-free if you don't also have a temperature or loss of smell/taste.
There will of course be exceptions, but likewise the government's 3 criteria do not also catch those cases that are mainly gastrointestinal. It is not a perfect testing system.