Oh OP, this has been such a pile on.
The rules are pretty straightforward. New, persistent cough, go get a PCR.
In your OP, you said you left after a couple of hours, and you asked if he should have just left after the 3rd or 4th cough. Then people ran with 'has he only coughed 4 times, get a grip, maybe he was choking'
Questioned you on whether you knew he had allergies.
Told you to get a grip a few times more.
The people that still don't know the rules is astounding. And the amount of people who think LFT's are the gold standard in covid testing. 'I've got symptoms but all my LFT's have been negative' Great! Now get a PCR as LFT are for asymptomatic cases.
Every day I have to tell someone that.
OP. You work in an office that allows to work from home, for situations like this. Cough starts, get a PCR.
I have had so many conversations with parents who insist on not testing their coughing teen by saying 'it's only a cold, it's not covid' like they have some sort of crystal ball.
We're over 18 months into the whole thing, and still the rules are a mystery to some.