I really don't think that it's related to the kennel. It was a contagious disease problem, the effects would last longer than 24 hours.
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.
This could also be a parasite problem. If you have not seen the vet for a fecal exam recenlty, you will want to do so to rule this out.
Let me know if you still have questions.