Hello and welcome to the community.
Yes, you can take any OTC cough medicine as far as safety and drug interactions go.
Even though your asthma may be generally well controlled, asthma can get out of hand very quickly with a respiratory illness.
You do need to use your rescue inhaler exactly as prescribed during colds to prevent a flare. Asthma doctors typically don't like their patients treating cough symptoms with regular cough medicine as they mask the symptoms of a developing flare. Any of the various forms of albuterol actually do work better than standard cough medicines for non-cough variant asthma.
Monitor your symptoms carefully and if things get out of hand, be sure to see your doctor quickly.
Feel better and God bless.
How are you? Do you still experience nasal congestion or difficulty in breathing? Antihistamine medication or decongestants may help provide relief. It is important that you rest and drink plenty of fluids and ascorbic acid. If it persists, it is best that you have this checked by your doctor for proper evaluation.