P.S. I do use an inhaler prior to every ride but I can’t imagine that this would be the cause?
Most anti-asthma drugs use a bronchial dilator and expectorant combo. This could be reason for the chest congestion needing to be expressed. Before your ride you may want to take something like mucinex to get most of your chest congestion out before your ride, or at least break it up so it comes out quicker. I wouldn’t make a religious practice though.
Benadryl can make you drowsy. If it is only after your ride I would take a banadryl or 2 as I pack up to leave. Those symptoms could very well be allergies.
I would also like to say that I am no doctor nor have I had any medical training. I would advise you to go see your doctor if this really concerns you.