URI's are typically caused by viral infections. Zenequin is used for bactial infections. Vets prescribe antibiotics to ward off any bacterial infections while their immunities are lowered from the virus. So Zenequin won't provide relief unless by chance his URI is bacterial based. If its a virus, it just needs to work out of his system. If it is bacterial based, give it a couple of days. Zenequin is strong stuff.
Take him in the bathroom with you when you shower so that the steam helps to unclog him. I have resorted to vaporizors when they get really stuffed up. And do what you would do when you have a bad cold - push lots of fluids, make sure he continues to eat well (use stinky canned food if you need to), and let it work itself out of his system.