Hospital incompetent?

We took our 3 year old to the hospital on Tuesday because she was having trouble breathing and said it hurts in the chest/lungs. We waited 5 hours and the Doctor on call just checked her out and said it’s pneumonia. And we got antibiotics and saline for inhalation therapy. He said to take her next week to our pediatrician for a follow-up. But I later read that to be determined if it’s really pneumonia they need to do X-rays. Or am I wrong here?

So last night after she drank carbonated citrus drink, she started coughing and full blown wheezing just like the first night. It looks like a Asthma attack rather than pneumonia! I’m angry with myself for not knowing what to demand and probably giving her antibiotics for no reason! I’m calling the Pediatrician first thing in the morning but I feel like LO has been misdiagnosed and medicating her, is freaking me out and feel so guilty. Anyone gone through pneumonia?