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Can I get a little more information about your kitty? How old is she? Any weight loss? Is she eating ok?
When I see coughing cats, my first concern is bronchitis--inflammation of the airways. This can be due to asthma or allergies, but sometimes just happens. My own cat was coughing for many weeks--extended head and neck and it sounded like a "hairball" cough. We tried hairball medications, but I finally took him in to my clinic and took an x-ray of his lungs. Turned out he had bronchitis and had been coughing so much he caused one of his lung lobes to collapse!
Coughing in cats can also be due to lungworms or heartworms. If your cat goes outside, lungworms are a possibility.
There isn't much I can recommend you do at home for a coughing cat. I would get her into your regular vet tomorrow for a full exam and chest x-rays. If it is something like bronchitis, then steroids will often help immensely. I have my own cat on them and just give him a dose once or twice a week.
Hope that helps. Please let me know if you have other questions.