My Son Is 3 Years Old And Just Started School

My son is 3 years old and just started school this month. Last weekend Sept 14&15th he had what we thought was just a cold running nose and cough with a slight fever only at night. We took him to the local clinic Monday the 17th and with him being incorporative he was prescribed cough syrup and an antibiotic azithromycin 4mls for one day he was kept home from school Monday and Tuesday. He seemed like he was getting better. But today Sunday 9-23 he wakes up coughing like he can’t stop and this continues on all day. I gave him the cough syrup prescribed about 10am, some children’s musinex about 4pm he took a nap and woke up about 6pm again by a coughing fit. Should I take him into the emergency room?