I know what you are talking about and I admit I don't know a lot, but I can tell you what I have read. First, the noise you are refering to is a reverse sneeze. "It sounds like a long, repetitive snort. It is entirely normal." (Vet On Call, a book I have)

Yes, dogs can have allergies. Sadie gets green goo in her eyes, ear infections and licks the pads of her paws, all caused by allergies. we give her ordinary people benedryl, and a vitamin supplement, both under the direction of our vet. We have not had her tested, becuase the medicine seems to help.. I would talk to you vet and seem if they think it is allergies, if medicine will help, and if they think the dog needs to be tested to determine a specific source of the allergy.

I think dogs can also get asthma, but I don't know anything about that.