It's understandable that the vet didn't offer antibiotics. They only treat infections, not toxicities.
What's important is getting your cat to eat and remain hydrated. Offer him some canned food instead of kibble (dry), even regular canned tuna fish if you need to.
The feline liver is unique in not being able to tolerate lack of food for very long. Upon ceasing to eat, no matter what the reason behind it, the body sends fat stores to the liver as a source of energy. The liver isn't adept at processing fats and they back up in there. The liver becomes sluggish or unable to function at all and liver failure may result.
This is called Hepatic Lipidosis or Fatty Liver Syndrome.
What may seem odd is that if your cat is of normal weight many researchers believe they can tolerate being off food slightly longer than an overweight cat can.
If he doesn't start eating in the next 12 hours or so, you either need to take him back to the vet for intervention and possible force feeding, or you might try a high cal paste available at most pet stores in the kitten care aisle. Put it on the tops of his paws or bridge of his nose where he'll lick it off to clean himself and get some inside.
It's a good idea to switch him over to canned food once he starts eating again anyway.
The best way to start with ideal nutrition is to read ingredients on the cans (yes, canned foods are better overall). Name brands are not important, but ingredients are. Meat or fish should be in the first couple ingredients and not plant products. For example, "chicken, chicXXXXX XXXXXver..." or "beef, chicken ...", you get the idea. Not "chicken by-product meal" "corn meal" , "wheat gluten" or anything along those lines. Greens or vegetables of any kind are a waste of space. Not all proteins are the same either. Looking for the protein percentage on the label is deceiving if most or all of it is from plant material or by-products.
Even if you choose a kibble to supplement the canned foods it needs to have a real meat in the first two ingredients. You might be surprised at what could be on ingredient lists of some very popular, very expensive cat foods. Many of these foods are no better (sometimes worse) than dollar store pet foods and what the public would be shocked to discover is that sometimes they both come from the same manufacturing plant, using the same formula and just varying their shape, color or size and packaging.
This was something that became apparent during the recent pet food recalls.
For more comprehensive information on feline nutrition, by a vet who specializes in this research and offers findings and suggestions freely, check this site: http://www.catinfo.org/
I hope he bounces back from this quickly. It's obvious you care deeply and are trying everything you can. Let me know how it goes.