I'm sorry to hear that your dog may have contracted Bordatella while Gerry was boarded.
As I'm sure you know, this is a very contagious upper respiratory infection that is pretty common in some settings, such as groomers or kennels.
The good news is that this is considered a 'self limiting' infection...meaning that it only gets so bad before it goes away on it's own...sort of like the human cold.
As a general rule, we don't even prescribe medications for it because it will eventually go away by itself as long as the dog is otherwise healthy.
That being said....unfortunately, no one can prescribe anything over the internet. Just like in human medicine, we need to have an in person relationship, and since we don't have one, it would be illegal to prescribe anything for Gerry.
Something you could do would be to turn on your shower very hot and shut the bathroom door. When it gets good and steamy in there, take Gerry in for 5-10 minutes. Often the steam will help loosen things up and ease the coughing a bit.
If the coughing doesn't get better in a week or so, or if you notice Gerry getting sicker, then you need to have him seen by your regular vet, but odds are it will resolve on it's own in a few days.
I hope this helps.