An 8-month-old baby frequently experiences coughing and dry vomiting, which may be symptoms of tonsillitis or gastritis.

An 8-year-old girl has been coughing and vomiting for more than 10 days, showing signs of fatigue, loss of appetite, and irritability. Blood tests show an elevated level of neutrophils. During the intravenous fluid therapy, penicillin and Pioneer cephalosporin were used, but the symptoms did not improve. How should the coughing and vomiting problem be handled?