Sounds a lot like whooping cough to me as well. Unfortunately, at best the vaccination is about 90% effective, with some studies suggesting it can be only 60% effective - so that means at best 1 in 10 children will still be susceptible to the disease. It always pays to be vigilant.

The good news is that at their age, the disease is not life threatening, although it can be quite disruptive, not the least due to lack of sleep! Unfortunately, medications do not usually help with the symptoms - antibiotics may shorten the length of time they are contagious, but the symptoms are caused by a toxin released by the pertussis germ early in the disease - so even eradicating the germ itself does not necessarily stop the cough.

Good luck with it.