Hyperventilation is a symptom not a syndrome. This means that the same problem can have many different causes including a variety of brain and respiratory problems that can need more specific treatment than
Re; stuffed up nose. There are nasal sprays that can open up the nose, like Nasalcrom, and steroid sprays like Nasonex. Also saline nasal washes can be tried; and an antihistamine nasal spray like Astelin. Its important the nose be open so you can breathe thru it to filter, warm and humidify air going to the lungs. A consult with an ENT may be useful.
Re; Chronic Hyperventilation Syndrome, see:
http://www.remcomp.fr/asmanet/edit9702.html
Hyperventilation syndrome and Asthma - Just think about it ....
"The respiratory symptoms associated with this syndrome include shortness of breath, usually described as "air hunger" - a need to take a deep, satisfying breath, accompanied by a feeling of difficulty in inflating the lungs-, a small dry cough, the impression of a tickle in the throat. Most hyperventilators tend to sigh or yawn frequently and typically adopt a pattern of thoracic instead of diaphragmatic breathing..........
In fact, the presence of asthma does not exclude the diagnosis of hyperventilation. Both conditions are frequently associated.....
The investigation of a subject suspected of hyperventilation syndrome should include a systematic questionnaire and a good physical examination with some screening test to eliminate treatable conditions : pulmonary function test including a methacholine or histamine challenge test, chest X-ray, EKG and biochemical test. If needed, other tests may complete the investigation such as a stress test, a coronarography, a brain CT scan or thyroid tests."