I've been prone to sneezing burning eyes, no redness and runny nose since 3 months non stop. Never had a history of allergies. What could be the cause?

See allergist. Unless you have been tested, you cannot rule out allergies. Yet burning eyes is not typical for allergic conjunctivitis and more suggestive of dry eyes or an irritant reaction to eye cosmetics (Mascara) and even infection. Vasomotor rhinitis is yet another possibility. Suggest that you consult an allergist.
Suspect allergy. Symptoms suggest allergy. A less likely possibility would be sensitivity to some chemical in your environment. See your primary care physician. He or she will be able to diagnose your condition or refer you to an allergist.