Can we sue for an unnecessary head CT scan ordered on my four year old son?

Our four year old son hit his head while playing with his six year old brother. We did not see it happening. It was reported to us by our nine year old daughter. Over the next hour our four year old says his head hurts. It is during the night so we take him to the ER. While sitting in our car in the ER parking lot we are discussing whether or not to take him into the ER. While talking about it our child vomits. We take him immediately in. After waiting for about an hour he seems to be doing well. I tell my wife that I will be back soon. I ran home quickly to clean out the vomit before it soaked into the seats even further. I had only been gone around 20-30 minutes when my wife calls to tell me he had a CT scan. The reason that I left to clean the car is that he looked normal. Had I been present, I would not have allowed a CT scan without even being seen by the doctor. When I returned to the ER, we waited longer for the ER doctor. The doctor examined him and said it was probably just a virus. Of course the scan came back normal. I am angry that a lazy and incompetent ER doctor sent a child for a head CT scan without first examining our child. I want to sue the doctor and the hospital for this gross incompetence. I do not want this to take place again. Our child has now been unnecessarily exposed to an increased cancer risk because of this lazy doctor. Do we have a case?