Baby's Arm Dislocated? An Eventful Day

Keeping the kids entertained during doctor visits...
What an interesting and long day today was for us.  We started really early because my son had an appointment with the allergist.  I don't know if it's all hospitals here in New York, or I still haven't figured it all out but it's all a waiting game when it comes to appointments.  We first make an appointment which is usually weeks, if not months away, followed by the waiting you do at the waiting area before your name is called, and even waiting for the doctor once in the room.  It's always been that way for us.  Hospital visits are always dreaded for us, and despite our allergy issues we don't go as often as we used to.  
It took about an hour and a half (or more) before we were actually seen by the allergist.  We were at the hospital at around 9:30 AM and ended up leaving around 2:30 PM.  We did a skin test to see if any changes showed up with his food allergies.  And lots of talking (the part which we really dislike!) My son was such an amazing trooper, impressing me with extreme tolerance, patience, and positivity throughout all that he has to endure at such a young age.  My little girl was all over the place like a toddler is expected to be, but was excited to finally leave. 
Unfortunately our day wasn't over yet, in the morning we had noticed some serious swelling on my sons gums that we had to get checked out.  We tried to get his dentist to see him but he was all booked, and it just wasn't lining up.  So being the worried parents we were, we decided our local hospital ER might be able to help.  We arrived at the other hospital, and waited in the waiting area for almost an hour - despite the fact that there was only one other patient waiting there.  I had hoped for an in and out visit, but no.  I had brought my kids food, so they ate their lunch, and then some snacks...  Soon both were just about to collapse from being so tired, specially my toddler who kept fighting her sleep.  My son was occupied sitting on his daddy's lap watching the cartoons they had on, but my daughter was everywhere and very cranky throwing herself everywhere.  Not being her usual self.  Change of atmosphere will do that to a baby who is tired, curious and can't fall asleep since there's so much going on.
At one point, she threw herself on the floor and I picked her up by her arms.  It was a gentle grab and hug, something I've done a hundred times before..but this time by the time she was in my arms she was holding onto her fingers and crying.  At first I thought it was just her being cranky and tired.  Rocked her back and forth, offered to nurse her, "wash" her hands (one of her favorite things to do) but nothing.  Something was wrong, and I was shaking terrified that maybe I accidentally bent her fingers or something.  Then I noticed her fingers were fine, but her whole arm wasn't moving - or she wasn't moving it.  She would stop crying and then complain again.
In a matter of five minutes of me completely freaking out (to myself,) I told my (much calmer than me) husband that I'm going to check her in to the ER too.  He assured me she's fine, and probably just cranky from being tired.  I managed to ask the doctor on shift in the ER about what she thinks I should do, and if she can take a quick look.  She looked at me, and without any effort told me to get her registered first.  Disappointed and worried I went back and forth in the lobby of the hospital registering her, even filling out her name wrong because I was so tired, worried, and scared.  Finally got her in, and then the RN would see her first to take her vitals and assess the situation.  By this time my daughter was even more irritated, and when the RN went to take her temperature under her arm she fought with her whole body including the arm that she wasn't moving before.  She cried some more.  And then the RN knew my situation and walked me over to the doctor to get my baby checked right away. 
By the time we got there, my daughters arm was all better!  She was moving it just fine, and suddenly in much better spirits.  The whole body tantrum moves must've gotten everything back to normal in her arm.  I was ecstatic that she was all better, but then I thought of the medical bill for this visit.  I wish medical professionals would treat patients more like people and less like a list or routine...  I think in the end the doctor felt bad for not just giving a slight care for a worried parent, who know maybe all of it could have been avoided.  All of a sudden the doctor asked about my son, still waiting in the waiting room just for his gums to get looked at and helped us get a referral to get seen by a dentist right away.  It ended up (luckily) that his molars are trying to come out and the top pieces of bumps we keep seeing was his gums just being torn.  
We ended our day with a trip to Toys R Us and let the kids pick out a toy each.   

I can't believe while I was waiting to be seen for my son, my daughter needed to be registered too!  Thank goodness they are both okay!  Ever have that happen to you?  Is this just a normal thing when you have more than one child?