Hi. I'm Dr. Lee and will do my best to help.
Based on these info, I would have to agree with your vet that there is a big infection going on. The white cell count is very high, and antibiotic is definitely needed. However, another problem is that the eosinophil is also super high at 6,636. This can indicate either a parasite infection, a severe allergy, or sometimes inflammatory bowel disease as well, which can cause vomiting and weight loss. I would suggest to go back to your vet and ask about this. IBD can only be diagnosed with a biopsy of the intestine, thus needing surgery. Treatment is usually via using special diet and steroid. Special diet is usually something called Prescription Diet z/d. I would also suggest to ask your vet to check the feces for parasites.
Please let me know if you have any questions or concerns. Thanks.
Exactly what antibiotic is he getting?
Thanks for the info.
With using Zeniquin for 3 days, I would expect there is some improvement. Since there is none, I would suggest to take him to another vet for a second opinion. At the very least I would suggest to do the following:
1. Add on a second antibiotic called Clavamox.
2. Change food to Prescription Diet i/d or z/d immediately.
3. Consider getting steroid to help in the interim.
Unfortunately all of these require going to the vet. So for now, all you can do is to keep him hydrated by making sure he drinks water. But he should definitely go to another vet as soon as possible.