Allergic to greenies?

My 11.5 year old pug/griffin mix dog has been having nasal/breathing issues for the better part of two months now. He was put on clavamox then Zithromax with hardly any alleviation of symptoms. His lungs are clear, no fever, no nasal discharge. He breathes out of his month and if you listen closely he makes a whistling type sound when his mouth is open. He has been a bit lethargic and we've had to add "human" food to his dog food to make sure he eats it. Most recently our vet put him on an asthmatic medication this past Tuesday and he's been doing fantastic since - all his breathing issues went away and he was back to his normal self without any of that junky congestion sound. I gave him a greenie tonight (he's eaten these all his life but hasn't had any for the past week or so) and shortly after he ate it all his congestion issues seem to have returned... He's breathing with his mouth again and it sounds like he's attempting to clear his throat. I'm wondering if he could be allergic to the greenie? I'm amazed at how quickly all his symptoms returned when he was doing so great the past few days. Our vet did suggest the possibility of a collapsing trachea or nasal blockage causing these issues but that wouldn't explain how he's been symptom free the last few days with the asthmatic meds only to have a sudden onset of symptoms return tonight. Any help is appreciated.. We are so stressed over this.

Thank you - just one question - if it was a dental infection would the asthmatic meds have made him better? He's much better again today and he seemed fine a few hours after he ate the greenie last night. I would just think if it wasn't asthma that the meds wouldn't help much.