I was finally diagnosed with viral asthma about 4 years ago (after being prescribed antibiotics and Ventolin) for several years. Every time I would get a cold, my body would not get better on it's own. A cold is supposed to last about 10 days - mine would continue and get worse for months. After trial and error, it was decided that I needed to take inhalers everyday (for the rest of my life), to keep it under control. Once it is controlled, it is not a big problem. I hope that your situation is a one time thing, but it did not end up being so for me. I am a healthy, very active person, so do not think that it is dire, if you end up needed to take medication. Best of Health!
I have heard of becoming steroid dependent. This is something I myself would like to look into. In this situation I would suggest try wheening off of it and see if your symptoms become worse. I don't think its wise to stop your inhalers if your asthma is on the moderate to severe side. In that case you may need maintenance meds for life. I too have had moderate persistant asthma since I caught a bad cold four months ago. My daughter had the same cold, and had a nocturnal cough for quite some time after that. Never before had it, and it just popped up out of nowhere. It is a very diversified lung disease and has many shapes and forms. Everyone is different, but even if you have no symptoms you still have inflammed airways.But having no symptoms means its controlled, and once you are there that is the safest place for you to be with this disease.
I worry about becoming steroid dependent, for life. I tried to (on my own) ween myself off of my inhalers, a few years ago, as I did and still do have trouble getting my head around the fact that I am inhaler chemicals. I ended up having to go on oral steroids, so I learned my lesson, that I cannot ween myself off. I don't know, but I was healthy until my mid-30's, then I caught pneumonia and have had these problems ever since. Again, I am very active (runner, cycler, etc.), with no history of asthma and have never smoked and I am on the light side (not overweight). This is why it took a few years for doctors to decide that I have adult onset asthma.
I developed asthma when I was 27 or 28 years old. It started after I had a cold. I severe asthma, and I am on Singulair and Symbicort. If your coughing does not get better, I would make an appointment with your doctor and see if you could get tested to see if you have asthma. It is a simple test that your physician can do in his/her office. If you do have true asthma, I would get him/her to give you an inhaler to try out.