"Pneumonia"

Last week I had to take my wife to the hospital due to big abdominal pain. The pain was so big she couldn't even walk properly. On the time we arrived there was a lot of people at accident and emergency department. We had to wait few hours which was understandable. Doctor did urine test, temperature check, blood pressure check, checked abdominal area as well. Didn't say diagnosis just prescribed Codeine and said that in few days my wife will be better. After few days she still had pain. She desided to go to private doctor. Private doctor diagnosed pneumonia and prescribed antibiotics. Now she feels much better. Question: why we have to pay to private doctor to find correct diagnosis if we are paying NI every month?