My 20 month old daughter has had a cough for almost 2 months now. She has been on one antibotic after another. Still has the cough?

Coughs linger. I assume that your daughter has been seen by your doctor and that pertussis ( whooping cough) has been ruled out. Viral illnesses do not benefit from antibiotics; and coughs can linger a few weeks. Is your child exposed to passive smoking, pets, dust? Is your daughter continuing to grow and develop along normal milestones? Any family history of food allergies? ;.
Chronic sinusitis ? Chronic cough can be induced in anyone with chronicsinusitis sincce the night drainage, which is inflammatory, can be aerosolized into the chest, certainly drain and inflame the larynx. This always needs to be excluded, in children particularly, but in adults as well!