In your case, no you could not get whooping cough from the vaccine. There are a number of types of vaccines. Some are based on killed bacteria or viruses. Others are based on toxins that the bacteria produce. Some are based on live organisms that have been weakened to the point that they cannot normally cause infection in a healthy individual or at most cause only mild illness
. These vaccines are not given to individuals whose immune systems are not intact (children, people with AIDS, lymphoma/leukemia, etc.). These "live attenuated" vaccines include measles/mumps/rubella, varicella, rotavirus, the nasal spray influenza (not the injection one). As you notice, the pertussis (whooping cough) vaccine is not on that list. That is because the pertussis vaccine is actually directed against the toxins produced by the bacteria, not the bacteria itself. This means that it has no infectious potential as there is nothing in the vaccine that could replicate. What can and often does happen after a vaccine injection is that the body initiates an immune response to the vaccine which is the whole point of a vaccine in the first place. It allows the immune system to recognize the toxin in the future and mount a more efficient assault against it. The bottom line is that this immune response is an inflammatory condition with the production of multiple chemicals that can cause feelings of illness (many symptoms of illness are in fact "side-effects" of chemicals that the immune system releases to fight infections). This typically lasts a day or two after a vaccine is given. If your symptoms last long than that, then you may have come down with an infection, though it would not be related to the vaccine. In this case you should see your primary care physician
and discuss your symptoms with him or her.