Welcome to Justanswer! I am Dr. Altman and happy to assist you both today!
I am sorry to hear Kami is having this cough that is productive.
There are some home remedies that can help reduce the cough and give relief
1.) The steam of the shower when the cough is severe or constant
2.) A little honey three times daily can help soothe the lungs
3.) If you have a humidifier or nebulizer that would also be wonderful to use in this situation
Unfortunately I prefer to avoid cough suppressants because when suppressing a cough if there is phlegm or buildup and lead to bronchitis or even pneumonia if the material is not coughed up so this is not something I tend to administer.
I hope this information makes sense! Since the cough is productiveI would advise a veterinary exam sooner rather than later to ensure reinstituting antibiotics are not warranted. This could potentially be allergy related or the medication she was previously on might have left her susceptible to infection which can have a 7-14 day incubation period (the steroids you listed)
Please let me know if I can be of any further assistance to you both!
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