I am sorry that you had such a rough week! When everyone is stressed, it does not make for a very easy time.
There have been a few times that I have been worried about my child, and no one really knew what was going on. How did I handle it? Well, I think the biggest point to make is that we are all human. Doctors and nurses are not gods and they cannot figure everything out all of the time. There have been times that I took my daughter home from the hospital, and no one could tell me really why she had ended up there in the first place (aside from vague references to her ongoing diagnosis).
But it is what it is...and I knew they would not send her home if she was not doing better. You just have to give it up and know it could have been any number of things that caused the fever, illness, altered mental state, etc...and you may never figure it out. That is a hard place to come to though!! I completely empathize with parents who want what is best for their child and can't find answers. The fear and the "what if this happens again" are very stressful things to think about.
I do remember when we started out with my daughter's medical issues, I did get frustrated when no one could give us answers. It is definitely a learning experience, and you have to trust that you are going to be given the best care possible, even if the outcome is not what you want. I personally would not trust a doctor who just handed me medications for my child as a way to placate me. I want to know that if the child needs medications, they will be given, and if there is no need for them, they won't be given unnecessarily. But that does require trust on the parent's part, and patience on the part of the doctors/nurses.
I have found that the more time a doctor spends explaining to me what they understand is happening (and honestly admitting when they don't understand!!) the easier it is to accept that there may not be an answer.
I want to say again that it has taken me a while to come to a place where it is not frustrating. If you are a parent in this situation, ask a lot of questions, even ones that you think are silly. If you are unsure about going home without understanding what happened to make your child sick, ask what to watch for, what to do if something happens, etc. Having a plan makes things easier. Ask if you should follow up with any specialists, or if anything needs to be looked into further at some point.
I always try to take a deep breath and know that my child is in reliable and caring hands and that everything possible will be done to figure out what is wrong...that she won't be brushed aside and our concerns won't be ignored as long as we all work together as a team.