This is a classic symptom of house dust mite allergy induced rhinitis. You need to consult an allergist near you.

Very clearly you are suffering from allergic rhinitis which is a allergic condition involving nose. Most common allergen for early morning allergy is pollen allergy as density of pollens in our environment is maximum in the morning hours. If your symptoms are continuous and not vary with seasons then you can use steroid nasal sprays once in night atleast for few months You can also use antihistamine tablets in the night. Practically its very difficult to avoid pollen allergy and medicines are most of the times a necessity