What do I do?

[Bogertophis]

...But he still “coughs” (I know snakes can’t cough). He breathes with his mouth open and he wheezes...

What might be happening is that he has damaged his nostrils, so he has to breathe with his mouth open. I had a bull snake that did some of this...he was another "pusher". The "wheezing" might just be the resulting sound of his breathing this way...especially since your vet found no mucus or bubbling in his mouth.