Sounds like an allergy type thing its called "reverse sneezing" and can be brought on by allergies there are some allergy meds available thru your Vet you should check with them about your concerns. This is a good time of year for allergies to show up as most of them are caused by environmental things.
I use Cytopoint for my dog she has environmental allergies it works really well and after a few shots can last a bit longer each time and safe for young dogs and puppies. Its expensive but if you compare the Apoquel its about the same. Apoquel gave my girl bad diahrea and upset stomach so I don't give her that at all.