You have a serious issue that needs immediate vet attention. The cat exhibits a dry cough repeatedly. However if your cat is lethargic and refuses to eat for more than a day or so or has had repeated episodes of unproductive retching you should consult your veterinarian without delay.
Most cats have hairballs regardless of the length of their hair. It is no secret that cats spend hours licking and grooming their fur. Diseased or painful teeth and gums can cause your cat to stop eating. Hairballs in cats are generally about an inch.