Wiktionary
went down the wrong way
vb. (en-simple past of: go down the wrong way)
Usage examples of "went down the wrong way".
Malone had trouble with cigar smoke that went down the wrong way, and by the time he'd downed half his drink in order to stop strangling, Mr.
Lothar drank greedily, choking and coughing as the water went down the wrong way.
Charlie coughed as some smoke went down the wrong way and began to pay closer attention as his host revealed the conversation that had taken place between Trentham and himself.