Is there any cure for allergies?

Possibly: Medications can improve the symptoms and decrease the immune response but the only way to resovle them is to be tested and undergo immune sensitization (allergy shots). You might consider seeing an allergy/immunology physician if you have not already done so but it would be best to start with your primary care physician for disucssion.

Is it allergies: As dr bessmer notes you have options for management if it is allergies. Many people under estimate the effect of airborn irritants & assume they have allergies when its not the main problem. Hair spray, perfume, cigarette smoke, gasoline fumes, cleaning fumes etc all effect your airway/nose & may triger identical effects. A lifestyle audit, aimed at removing such irritants can help a lot.