There are a number of different causes for a cough that goes on as long as this, but you should definitely see a doctor
to help you sort it out.
Allergic rhinitis, or nasal allergies, involve inflammation and swelling of the nasal passages, leading to stuffiness, mucus, and chronic cough.
Sinusitis is an inflammation of the cavities in the skull brought about by plugging with mucus of the normal passages by which the sinuses drain into the nose, leading to congestion, headache, a sensation of fullness, and cough.
Heartburn, or reflux disease, can also provoke a chronic cough as the acid from the stomach washes up into the mouth and irritates the back of the throat.
Finally, in someone taking care of small children, I would also worry about the possibility of pertussis infection, or 'whooping cough', which causes a very strong cough that lasts for weeks and is often severe enough to cause soreness in the chest and ribs and may lead to gagging, retching, or vomiting
I suggest you start by calling your primary care doctor
and setting up an appointment. They will most likely be able to tell which is the cause of your cough and will help you decide on a plan for treating the problem.