There is a
commonCommon cold medical entity called vasomotor
rhinitisAllergic rhinitis. This is when the blood vessels lining the
noseNose fracture and sinuses are inflamed from a nonallergic condition. Certain stimulants increase the blood flow to the
noseNose fracture and there is a drainage that occurs either as a "runny nose" or post nasal drainage. The most common stimulants for increased blood flow are running, emotional stress, spicy foods and irritating odors. This probably has nothing to do with the shortness of breath you feel with activity, but can explain the drainage.
As far as the exercise, I would start with a very limited routine and build up slowly and gradually and see if this allows you to perform better without being short of breath. If this persists, seeing your physician to evaluate your lungs is a good idea.
I also have eczema on my legs and am on Allergy shots. When I first began to take the allergy shots 2 years ago is when I remember the symptoms first appearing.
Thank You