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Daily vomiting, especially food after eating and on different kinds of food makes me concerned that she has a primary GI reason for vomiting. The two most common in a 12 year old cat would include inflammatory disease or GI lymphoma. Other potential causes would include pancreatitis, kidney disease, liver disease or other metabolic disturbances. I recommend hat blood work be performed and referral to a specialist if you are not getting answers or treatments that help. Unfortunately, the only way to diagnose IBD or GI lymphoma would be with a biopsy and not all veterinarians are able to do GI biopsies. In the meantime you can try an anti-nausea medication which will only be a bandaid and not a permanent solution but may help her to feel better in the short term while you are able to get her to the right veterinarian.
Does this address your concerns tonight? If not, please feel free to ask ay further questions you have.
I don't think that the vomiting is "nothing". I think you should seek a second opinion from a veterinarian that is willing to recommend diagnostics. Perhaps an internal medicine specialist. Chronic vomiting despite diet change is concerning as this s not considered "normal".
The clinical signs of diabetes are weight loss despite a ravenous appetite, drinking a lot and urinating a lot. Also high blood sugar that is repeatable and sugar in the urine and/or ketone formation.
I am happy to talk about this more when you have time. I cannot recommend a specific diet in the meantime, however you may try a single carbohydrate and single protein source. Keep in mind that diet alone will take several weeks to see an effect.
I'm glad I could be of service. Please feel free to return if you have further questions.