Hi there,
I am sorry your kitty is ill. He needs to see a vet ASAP. I am concerned that he is not eating and vomiting. It is good that he is playing, but he will not be able to sustain himself if he does not eat enough. Also, his liver will start to shut down if it does not receive adequate nutritional support.
Young cats will vomit and have decreased appetites for several reasons. Most commonly would be intestinal parasites. Your vet can run a fecal panel to diagnose any parasites present and can prescribe a parasite specific dewormer that would be safe for your kitty. Next on the list would be intestinal foreign body. This is an emergency, and requires immediate medical attention. Your vet can take some radiographs to look for obstructions and can guide you on the process (surgery) of making your kitty healthy again.
Please have your kitty seen tomorrow so that he can get the medical attention he needs, and start to feel better soon. If this has been helpful, please hit the green accept button. I am here if you have further questions or if you need more advice. Best of luck with your kitty!
Emergency Critical Care Nurse
16+ years of veterinary experience