Hi and thanks for your query,
You certainly have asthma and the management of asthma involves utilization of many drugs. Its not only the drugs that matter as far as the clinical outcome is concerned, but in some cases, some of these drugs might need to be taken chronically for some time before clinical measurable results are seen.
It shall be worth consulting a pulmonologist. If he realizes that the allergic aspect of your symptoms is predominant, a coordinated joint management between your pulmonologist and an allergist could be beneficial. I suggest you consult a pulmonologist and suggest integration or an opinion of an allergist.
Thanks and hope this helps,
Luchuo, MD.

Hi,
thank you for query.
Allergic rhinitis or hay fever may follow when an allergen such as pollen or dust is inhaled by an individual with a sensitized immune system, triggering antibody production. These antibodies mostly bind to mast cells, which contain histamine. When the mast cells are stimulated by pollen and dust, histamine (and other chemicals) are released. This causes itching, swelling, and mucus production. Symptoms vary in severity between individuals. Very sensitive individuals can experience hives or other rashes. Particulate matter in polluted air and chemicals such as chlorine and detergents, which can normally be tolerated, can greatly aggravate the condition.
Characteristic physical findings in individuals who have allergic rhinitis include conjunctival swelling and erythema, eyelid swelling, lower eyelid venous stasis, lateral crease on the nose, swollen nasal turbinates, and middle ear effusion.[17]
Even if a person has negative skin-prick, intradermal and blood tests for allergies, they may still have allergic rhinitis, from a local allergy in the nose. This is called local allergic rhinitis.[18] Many people who were previously diagnosed with nonallergic rhinitis may actually have local allergic rhinitis.[19]
The management of rhinitis depends on the underlying cause. High-dose administration of Vitamin B12 has been additionally validated to stimulate the activity of the body's TH1 suppressor T-Cells, which then down-regulates the over-production of the allergen antibody IgE in allergic individuals which could decrease both near and long term manifestations of rhinitis symptomology.
so prevention is better than cure.