Kitten can't keep food down

Alright so I've scoured the internet for information, and can't find anything that fits my situation close enough, so I thought I'd come here and see if anyone could offer any insight.

Here are the basics:
-Last Monday (March 14), my kitten Jax when in and got neutered. He handled the surgery fine, they said he was great with the anaesthesia (they kept him for the full day so my wife and I didn't actually see how he handled it), and they sent him home the next day with some pain pills and amoxicillin.
-We followed his prescription to the letter for the week and had no issues Tues-Thurs
-That Friday (March 18), after getting his amoxicillin and eating a bit, Jax vomitted. It was only a little and didn't seem to affect him, so we kept an eye on him for the day and he was fine, continued eating, and was his normal self. We called the vet as a precautionary measure Saturday morning and he told us that it could have been a minor reaction to the amoxicillin, but just to continue his prescription and keep monitoring him. Jax was fine for the rest of Saturday.
-Sunday (March 20) Jax got his pill again in the afternoon, then ate and vomitted again. We became worried but continued to watch him, and a few hours later he ate again and shortly after vomitted yet again. Not wanting to take him to the emergency vet (and observing he was absolutely 100% normal other than the vomitting), we just kept an eye on him until Monday.
-Yesterday, Monday, we took Jax in to the vet who did a thorough check of his abdomen for foreign objects, checked his gums, checked for signs of pain, checked his breathing, took his temperature, the works...he basically checked everything he could physically. At home Jax was still completely normal, playful, hyperactive, but didn't want to eat more than a few bites of food at a time (presumably for fear of vomitting), so in light of this and the clean bill of health as far as he could see, the vet gave us some vomitting medicine and told us to use it for 3 days and see how he did.
-Today we had the idea that perhaps Jax wanted his old food back (we use Science Diet, but switch between 2 flavors so he doesn't get bored...he's very picky). As soon as we gave him the food, he attacked it and ate more at one time than we've seen him eat in at least 24 hours. We were ecstatic, thinking the nausea was just a side effect of the amoxicillin (which we stopped giving him Sunday as per vet's instructions), and the eating was just him being picky. However, about 15min after eating, Jax went to his litter box and vomitted yet again.

At this point, my wife and I are nervous wrecks, having absolutely no idea what could possibly be wrong with him and as usual fearing the worst. The doctor said to keep up the medicine for the three days until it's gone, then bring him back if he isn't better, and it's only been a day, but there should be no reason he can't keep food down. Again, other than not wanting to eat and/or vomitting, he's very playful, energetic, and affectionate as he always is. If anybody has any constructive ideas, or insights based on personal experience, they would be greatly appreciated.

It's most likely the new (old) food causing the problem. Switch back to what you've been feeding him prior to the Science Diet. If you want to change his food, do it very gradually over a period of a few WEEKS. However, until he's no longer throwing up, don't change his food. You might offer him some shredded boiled chicken (boil a chicken breast or thigh in plain water, no seasonings) or even meat baby food (no onions or garlic or mixed with anything else).

It probably is due to a few things stress from the surgery..Antibiotics and often Anaesthisia causes upset stomachs..When I had my Persian neutered this fall he vomited for a week after. Not alot but abit daily and other wise seemed fine.
Just keep a watch and hopefully this will pass and back to no vomiting soon.

It could also be just a throat irritation as they tube these kitties for the surgery. Give him something to coat his throat; plain yogurt, just a tiny bit of vanilla ice cream, cream cheese, spray cheese, or white bread cut into tiny bits (crust removed) and soaked in a bit of milk. Only give him one of the above and see if it helps.

A little update:

We bought some Hill's canned food from the vet, they suggested giving him that to see how it worked, and he seems to be doing much better with it. He's eaten half the can in the past 2 and a half hours or so, and has kept it down and been running around playing.