Have Cat Questions? Ask a Cat Vet Online.
This could be a simple case of reflux. You should see the vet tomorrow to find out for sure. If this is the case, your vet can prescribe an antacid that will help a great deal.
Until then, you can use a dose of hairball remedy right before meals. This coats the throat and helps with acid build up.
You will also want to feed the cat several small meals a day and see if it helps. Jarred baby food works well and is mild enough to soothe the stomach. Try to stick to chicken/rice or another bland food with no garlic or onions.
Your vet might want to prescribe tagamet to help with the reflux.
Any time that a cat will not eat, you should be very worried. If a cat won't eat for more than 48 hours, you are in serious trouble. Their liver can fail and then the cat can die. It is called hepatic lipidosis where the liver thinks it is being starved and starts "grabbing" fat cells...and actually ends up killing the liver.
I suggest that you see the vet first thing tomorrow for a full exam and possibly bloodwork to find out what's going on.
Let me know if you still have questions.