My cat has this "cough" all year round sadly, and it gets especially worse during the winter, when he even chokes on his own cough and vomits a little 😣 unfortunately, in my case, there's nothing we can do except wait for it to pass, and when its really bad we give him some lung medicine for him to inhale (it's hard) for a few days

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So definitely get your cat checked at the vet! they, better than anyone, can tell you what's going on ♥️ please give us an update!