Hi Sam...
I have had this experience several times. It could be something as simple as hairballs and can be alleviated with a common hairball remedy. Several years ago I rescued a 7-month old kitten and he was found to have a severe case of roundworm when I took him to the vet; he too kept coughing after he drank water. I currently have a 7-year old rescue who will cough after he drinks water that is too cold; he has a mild form of asthma. I would highly recommend you contact your vet again if the symptoms persist. A resourceful website (besides this one) is
Cat Cough - good luck with your cats! ~K