In response to your question, the morning congestion
is probably cleared with one breath or cough because it is in
your large upper airways and not in your lungs.
There need not be just one cause and it is also possible that with your strong skin test responses to a variety of allergens, allergy may also be a causative factor. The first reaction, in that regard, would be to reduce, partially or completely, your exposure to those allergens, particularly the mites and cat dander.