Hello and welcome. Finding this site was a good start. You will find lots of info here. I have learned alot from all of the wise parents on this site. You will receive lots of support and kind words.
I can only speak from my experience. I actually got a lot of help from the school and The Board Of Ed. My daughter's first evaluation was done through the school. She ended up in the Boce program and from there I was advised to take her to a children's psychiatric. hospital. for a full evaluation. So I did. I want to tell you to speak to the school psychologist, that's how I got started. However, every school is different. I have had very good experiences with my school district. They helped me alot. I do know people that have gone to their school district for help and instead of helping the school pointed fingers and blamed the parents. So be careful. Since you are having a hard time finding a pediatrician, my suggestion would be to try to find a hospital., most of them have out-patient clinics for mental health.
Good luck and keep us posted