Neurology is a tough science. It's fundamental to our existence and difficult to accurately assess. You want a physician that has the experience, the knowledge, and the willingness to try new things. This is especially important if you need to choose a doctor for one of your children.
I recommend you read about the doctors online, get referrals from your primary care doctor and family or friends. If you don't seem to be getting better, it's always okay to ask for a second opinion and seek information for yourself.