Has anyone had their child have a cough for 3 months?

Yes: It can be allergies, asthma, heartburn, infection, aspiration of foreign object, many things, but anything lasting that long should be checked out.

Yes: Sinusitis, allergy, asthma, exposure to smoke, heartburn, and whooping cough are common causes.

Many things: Sinusitis, allergy, asthma, exposure to smoke, heartburn, and whooping cough are common causes as dr belilovsky mentioned. Also consider a cough tic, particularly if not at night. Consider chest and sinuses xrys to ru;le out hidden infection. And of course see your pedatrician.

Yes: I really persistant for 3months, you need to see a dr. If only having a cough for a week or two then goes away for a short term and then comes back, may just be recurrent viral infections. But if persistant the reasons could be numerous from pertussis, asthma, sinusitis, foreign body swallowed etc.