I also use the public school system for speech therapy. But definately appeal.
Doctors are a dime a dozen.
A good doctor who will fight for you is worth their weight in gold. Go see a different specialist if you were uncomfortable with the fist guy. And ask questions before you go. Have you any experience with special needs kids, what are your qualifications, What ages do you generally work with. I have found ,and this is just my personal experience, the therapist who have worked in the school system and are now working in a private office are generally better at dealing with kids and parents and see the whole package better.