Why do I start sneezing and eyes watering after jogging/walking a mile or two?

Pollen allergy. If this happens when you're exercising outdoors it may be a pollen allergy. Perhaps you follow the same course everyday and are passing a particular tree to which you are allergic. Try a different route for starters. Also try exercising indoors to see if symptoms are related only to being outdoors. Let your doctor know the results of your experiment.
Non-Allergic. You should also consider non-allergic causes of sneezing and conjunctival symptoms such as vasomotor, cholinergic or gustatory rhinitis.