Lucky with health care....(sick child)

OK, with Hubby in the military, we have it pretty good with health care. As in pretty much free for everything necessary and some co-pays for non-necessary..but that doesn't mean that my child is not sick!
This past weekend, Cee started REALLY coughing. She has had a tickle in her throat for awhile but this was much worse. She couldn't walk across the store or laugh without hacking up a lung. So Sunday night (early Monday morning), I called the 24 hour nurse advice line and got no good advice. Not that the nurse didn't try, but where am I going to get a humidifier at 1 a.m.? My hubby is away so I should go to Wally World? Take my sick baby (11 yr. old) out? Basically, I wanted to know what meds she could take (that I had available) that would at least get her to sleep without killing her. The nurse was not keen on combining meds (probably a good thing) but to my sleep-deprived mind, I was getting nowhere. She would not give us authorization to go to the ER because it was not an emergency. Cee finally fell asleep because of the Benadryl and I was able to snooze for 2 hours at a time. I kept getting up to check on her. I took her into the doc the next morning and got something that helps and the cough is almost gone.
Then on Tuesday at gymnastics practice, Cee smacked her right arm on the balance beam. She told me about it but since she had continued practicing, I did not think it was that bad. I sent her to school on Wed. and didn't think anything of it. She came home after school and was in pain. So again, I call the nurse line. This time, I want to go to the ER for Xrays. Let's make sure the wrist isn't cracked, etc. Nurse wants to give me home care advice. I want authorization to go, she gives advice. I finally insist on it. She doesn't know my child like I do. My Cee plays HARD. If the wrist is cracked, she'll finish the job and break it somehow. So finally, against the nurse's advice, I take her for xrays and it shows that there is no cracks or breaks. So the nurse was right. But does this mean that I shouldn't have insisted on xrays? Did I over react? The ER wrapped her wrist and now it feels better. Is this a placebo effect or was the wrapping necessary. I ask all of this because I am not objective. When my child is hurt or sick, I can't be. Maybe I am too close to the subject but when she cries (for real), my heart literally hurts. Let me hear your honest opinions on this one...