Agree with Dragondawg
I agree with Dragondawg that it is a genetic condition found in the Maltese breed. It may be due to past "in-breeding" in a previous generation. The true cause may be hard to determine.
However, I would like to address another issue with the dog's "hacking issue". This may be due to an enlarged "uvala". (forgive spelling). Dog's have the same thing in the back of their throats as humans. Somethings they are too large and can block air flow after intense exercise. This may explain some of the other symptoms after this happens as the dog is being derpived of oxygen.
Has the dog had any surgeries? This condition is usually found during a surgery procedure when they put a tube in. You may ask the doctor to examine and see if the uvala is too big or if it was noticed at the surgery. It may have gotten irratated during a past procedure.
My dog Scooby has this but the vet told me he did not observe an enlarged uvala. However, it was difficult to make him "re-enact" the condition on the spot for the doctor. For some reason, running around in circles in the vet's office was quite embarrassing for the both of us to get him to show the vet.
My suggestion is when the "wheezing" episode starts. Stop the exercise immediately. I do a slight "heimlich" manueaver. I gently wrap my hands around his diaphram and push up. I treat it as if he were "choking". It tends to help end the episode a little quicker.
Most vets will prescribe tranquilizers for the other condition. Until the frequency of the seizures increase, no anti-seizure medicine maybe prescribed. Scooby has had a few tranquilizer shots himself over the years. 
Good luck with your baby. I know it is tough to watch. I don't think he is in pain for the most part. It may be more of fright than of pain just like you. Just give a good hug and love.
Scooby, Shaggy the "Dogs", Ms. Thang the "Cat" and introducing Measley Weasle "The Ferret".
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