Luckily my cats have never had any reactions to their vaccines but it can happen. All cats that get a leukemia vaccine at our office have to wait in the office for 20 minutes after the vaccine is given so we can watch for any reactions and the owners are told that if there is a reaction at home, to call us and bring the cat back in. I've only seen this happen a couple of times. I would call the vet and let them know what went on so that they can update your file with this information.
Good luck and I hope he's feeling better.