He was neutered two weeks ago, so I don’t think his symptoms are related to the surgery. You are doing the right thing by taking him to the vet. Don’t be scared. You are taking action and you will get your cat treated. He will be fine you’ll see. I’m not sure why he is vomiting but I’m positive it will stop. Please keep us updated and let us know how the vet visit went as soon as you can. I’ll keep my fingers crossed for you. I can tell you love your pet very much.
It is extremely unlikely that it is related to his neutering. Vomiting is not a symptom associated with UTI. That would show as a change in urination (more or less frequent, apparent pain or difficulty urinating, excessive licking of genitals, etc.). It could just be something he got into or that disagreed with him or that he didn't chew well enough. If the vomiting persists, I would check his stool for any changes (color, consistency, frequency, etc.) and contact your vet.