The coughing/choking/gagging is common for yorkies. They have a sensitive trachea and you must be careful when walking them on a lead. You should never use a collar with a lead; only a harness. Their trachea's can collapse very easy.
My Chorkie (chihuahua/yorkie mix) does this when she runs around, plays and gets too excited. I wouldnt worry too much but its worth getting checked out just in case.
