My one-year-old has had the same sort of cough, which caused him to vomit, and which started in October.
People can still get whooping cough even if they've had immunisations, but it's always a much milder strain.
My extended family had to fight tooth and nail this summer to get the diagnosis of whooping cough. In the end it was only diagnosed with lab tests because the GP was adamant that it wasn't whooping cough! You don't always get the typical barking noise with it, especially in the milder forms.
Interestingly, as far as I'm aware, using antibiotics for one week only serves the purpose of shortening the infectious period from 21 days to 7.
As with any respiratory problem, you would need to seek urgent attention if it becomes extreme in any way.
They say whooping cough is the hundred day cough, so we've got a little way to go before it fully clears us if that's what started last October!
Having said that, I had a cough in May which caused me to vomit (and lasted very long time) and which I suspected was whooping cough. And then I had the October cough along with my children, so both can't have been whooping cough, which does suggest that one of the coughs (either May or October) simply mimics whooping cough.
Either way, as I said earlier, my view is that it's a simple case of 'watch and wait', but have a low threshold for any worrisome symptoms that develop and seek help immediately if you're concerned about DC's breathing.