thats the trouble

kennel cough
cat flu
gongestive heart failure
viral infection (too many to name)
asthma
other bacterial infection (too many to name)
paracites
obstruction or something caught in their throat (grass seed etc)
hairballs

sooo many possibles, that its impossible for anyone here to diagnose, were not qualified enough, and even if we are an online diagnosis is unprofessional...

This isnt aimed at being nasty to the op... but hopefully the next person coming accross thisthread with acoughing cat will go directly to the vet, wont pass go and wont collect their £200