Hi XXXXXXXXX. Dr. Hurst here.
Any time a cat is exhibiting open mouth breathing they are in serious respiratory distress! She needs to be seen immediately by a veterinarian. Try to stress her as little as possible.
There are a number of possible causes including heart disease, cancer, FIP, pneumonia, feline asthma, heartworm disease, etc. Regardless of the cause, this is an emergency and she needs help so she can breath.
She may require oxygen to stabilize her, then they will need to take a chest film to try to determine what the cause may be. They may also need to do a thoracocentesis if there is evidence of pleural effusion. If fluid is obtained this can be examined to try to determine the cause as well.
Best wishes and let me know if I can be of further assistance.
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Cat Veterinarian
12 years as a practicing small animal veterinarian, including a feline only practice