Hello I am Dr. Joey. Thanks for trusting me to help you and your pet today. I am a licensed veterinarian with over 15 years of experience. I look forward to working with you.
Homeopathics are certainly a option to look into, but I must first say although there are options first it is important that our diagnosis is correct and I assume this diagnosis was arrive at after your vet sampled her lungs (either tracheal wash or bronchoscopy for both cytology evaluated by a pathologist and culture to ensure no bacterial infection). As long as we feel this is truly bronchitis, then homepathics are possible. I recommend if you want to pursue this route to get your vet to refer you to a veteirnarian that specializes (and has special training) in this area. This is not a do-it-yourself project as these drugs must come from good sources and be properly dosed.
Although not considered "homeopathy", if you are interested in Chinese herbal therapy there are some herbs that might help such as Liu Jun Zi Tang and San Ren Tang made by Kan Essentials. These you really must get from a vet that works with such products but I have seen improvement in some tough cases. There are western herbals that might help like Mediherb's Brochifect and Andrographis complex.
A true homeopathic utilizes diluted, but energetically potentized substances prescribed in ways that are unlike our thinking in conventional medicine. So if you are interested in things like herbs, nutritional supplements, etc, I recommend get a consult with a vet who practices alternative medicine. The type prescribe would be carefully calculated and determined based on her exact diagnosis and clinical findings.
There are no over-the-counter homeopathic remedies that I can recommend without a thorough evaluation of her history, testing performed and an exam. Homeopathics are "drugs" just like what you are using so it is not something I recommend dabbling in without expert help. :(
Now, if she has not had a tracheal wash or bronchoscopy, then this is a next step to try to get an exact diagnosis and confirm this is actually bronchitis, and not another problem like fungal infection or cancer. If bronchitis does not respond to traditional therapy (prednisone) then allergy testing and then treating for underlying allergic disease with allergy shots is one approach.
From a traditional medication perspective, I usually always use both an antihistamine and corticosteroid (pred) in the beginning. Some dogs benefit from a drug like theophylline to help with the coughing as well.
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