Welcome to Just Answer. IF Disney is able to drink water and eat his dinner without trouble, then there most likely isn't' something caught in his esophagus. If you believe he has something in his trachea, that is pretty rare. I'm very suspicious that your little one has kennel cough. That is a viral/bacterial upper respiratory infection of the trachea that causes irritation and coughing events like your describing. Here is a video of a dog with it.http://www.youtube.com/watch?v=zx7tveHyFqkIf this is what is going on, then his body is fighting of that infection. If there is no nasal discharge then most likely it is viral at this point. If there is discharge then there is a secondary bacterial component. These are cases where I will recommend antibiotics to be given. If the coughing is persistent and she can't get comfortable, then cough suppressants can be used. These should both be obtained from your vet. Here is a great link on kennel cough.http://www.veterinarypartner.com/Content.plx?P=A&S=0&C=0&A=600
PLease let him rest and don't stimulate him. No smoke or dust as that can make it worse. Also no leash walks - use a harness.
I was hoping that's what he sounds like. In all honesty, as long as he's still eating and drinking, resting comfortably and not having tons of nasal discharge - he most likely doesn't need any medications. If he gets worse, your vet will want to start up oral antibiotics to help fight a secondary bacterial infection. I wouldn't do any cough syrup at this time, some coughing is good to help clear the mucus out of the trachea. Kennel cough cases can take 4 to 10 days to get better. The doggy day care is where he most likely was exposed to this.