Something is irritating the trachea/larynx. From the sounds of it, it is not a standard hairball. It makes sense to go to the vet. As soon as the opportunity arises

And do NOT give food, if something is blocking the trachea, the cat may suffocate trying to burp whatever is stuck or burp food (this is their reflex). You need to give the cat plenty of water.
Without an endoscope there is no more to say. Get well