Hi there, I'm Dr. Sara. I'm a licensed veterinarian who works exclusively with cats and dogs. I'm sorry to hear of your frustrating experience so far in managing Jambi's vomiting - I'll do my best to help.
Chronic (long standing) vomiting in kitties is a very common complaint. The very first thing that I consider with chronic vomiting kitties is dietary sensitivity. Just like your vet, I usually start by making dietary recommendations. I suggest that vomiting kitties avoid all things fish and seafood - they have been shown in research to contribute to inflammation in the gut and vomiting. Food sensitivities can cause vomiting at any time of the day, not just immediately after eating, because they inflame the whole GI tract for long periods of time - not just right after they eat. My favorite over the counter foods for vomiting kitties are Natural Balance's Limited Ingredient Diets (they have multiple flavors) or Nature's Variety's Instinct diets.
I usually perform both blood work and a broad spectrum deworming (like Profender or a course of fenbendazole) at the first visit with my vomiting kitties and recommend a diet change, followed by a recheck exam in about a month as long as they stay stable. If they aren't doing better at that point, I may recommend a prescription cat food like Royal Canin's Hypoallergenic Select Protein diets to further investigate for dietary sensitivity or suggest an X-ray and/or abdominal ultrasound. If the blood work was all normal, then I'm suspicious that we may have inflammatory bowel disease, which can be tricky to diagnose without biopsies. In a young cat or a cat with severe signs, I do recommend getting intestinal and/or stomach biopsies, and possibly run some tests to check pancreatic function. In an older cat I might discuss a trial of prednisone with the owner. Prednisone treats for IBD and it's usually quite effective, but it is usually a long term maintenance medication and can have some undesirable side effects such as predisposing the kitty to becoming diabetic. The choice on whether or not to begin prednisone is one that is individual to each cat, client, and situation. If they respond well to prednisone but relapse and start vomiting after we wean off the pred, I'll sometimes also consider trying a drug called budesonide. Budesonide is a steroid that is not absorbed as much through the intestinal tract into the blood stream but can have local anti-inflammatory effects and help keep the vomiting under control.
In older kitties, chronic vomiting can be a sign of GI cancer like lymphoma (which would be most common), as well as others. Without investment in an abdominal ultrasound or scoping, it's difficult to prove one way or the other. As the most commonly encountered cancer that causes vomiting, lymphoma does also respond well to prednisone treatment. The difference between IBD and lymphoma, though, is that the lymphoma usually only responds temporarily to the treatment and then the vomiting starts again.
I sure hope that this info helps - please let me know if I can answer any other questions for you - we can continue to chat until I've covered them all!