I can understand being upset. Let me try to reassure. Sometimes, not treating is the appropriate protocol. For reasons unknown, sometimes infections spontaneously "disappear". Sometimes we believe the body is able to fight them off. Other times, the sputum culture could have contained bacteria from the nose or mouth, or environmental contamination.
In those cases, "watch and wait" is the correct approach.
Have you asked your doc what the plan might be?
Sue