Son takes steroid inhaler and zyrtec (cetirizine) nightly for asthma. Since allergy season started, cough returned & albuterol won't get rid of it. What can I try?

Peak flows. Please use a peak flow meter to help document how your son's asthma gets better or worse. With these data, you can work with his pediatrician to make an asthma action plan, which can help to guide the correct use of different medications. It may be that he needs a burst of oral steroids, but difficult to say without numbers.
See doctor. This suggests that your son's asthma is spinning out of control. You need to talk to your doctor to check out the cause for the coughing which may originate from gerd or even a sinusitis if asthma turns out not to be the reason.