See a pulmonologist. Allergist will treat for allergies, and may or may not test for asthma. You need a complete lung function test. Yes, you may have allergies, and they may trigger asthma. Or you may NOT have allergies. It is also a good idea to be tested for allergies, as they can be triggers for asthma.
Years ago I was diagnosed with vaso-motor rhinitis. Which means I react as if allergic to changes in temperature and humidity, anything that is in the air. But I am not actually allergic. I've been tested several times, and never come up allergic to anything. Temperature and humidity are big obvious triggers, stuff in the air is less obvious, but definitely an issue. Anyways, all of this triggers my asthma which was diagnosed when I was in my 30s.
Long term control meds help big time. A peak flow meter to monitor your breathing ability. Coughing is the #1 symptom of asthma, yet many doctors ignore it as an asthma symptom, thinking "upper respiratory infection."
I am not overly fond of the tessalon pearls or any cough suppressant. The cause, not the symptom is usually what needs to be addressed. A bronchialdilator (sp?) that will open your airways and allow you to breathe is MUCH better.
I take advair, singulair, daily, with xopenix (levabuterol), claritin and sudafed as needed. Prednisone several times a year. There are other meds, and your doctor will figure out which ones work best for you. I have n inhaler, but only use it when I am out. I also have a breathing machine which is MUCH more effective.
And when you are really ill, and need rest? dh MUST take over and see that everything gets done and that nothing falls apart.