My cat is throwing up and not eating dry food. Should I be worried?

Hi and thanks for using Petco Pet Education Center, formerly Petcoach! Sorry to hear about Simon. It's hard to say if you should be worried at this point but if the vomiting continues you will have to get him evaluated. Any sign of illness in a pet that persists or worsens needs to be evaluated by your veterinarian and re evaluated until the problem is resolved. Vomiting causes fluid loss and electrolyte loss and can lead to dehydration and weakness. Not sure if Simon is an indoor/outdoor cat but I would advise deworming him since intestinal worms are so prevalent. That is an easy thing to do to rule out intestinal parasites and should be done in all cases of gastrointestinal upset as long as the medication can be safely given and it is not vomited back up. Intestinal parasites are extremely common across the globe and account for the vast majority of vomiting and diarrhea cases. Other causes include inflammation, infection, dietary problems (including dietary indiscretion or eating things pets are not supposed to eat, food sensitivities/allergies), ingestion of foreign bodies or exposure to toxins, bacterial overgrowth in the gut, problems in the stomach, intestines, or even problems outside of the intestinal tract/stomach including pancreatitis, kidney/liver problems, metabolic disease (diabetes,etc), endocrine diseases (thyroid or other hormone problems), etc. A thorough history and physical exam with resultant diagnostics such as fecal tests, blood tests, and more imaging studies such as x-rays/ultrasound to try to determine what is going on. Good luck with Simon. I hope this resolves quickly with little effort.