We had two children go through this and had hugely different experiences. I'm still not sure whether that's down to different problems or different counsellors.
DS1 (Asperger's, OCD, phobias, eating disorder) waited two years to see anyone who felt qualified to help, but when he finally did, it's not overstating it to say she turned his life around.
DS2 (theoretically NT, overanxious, bedwetting, saying he wanted to be a girl, talking suicide) was seen in weeks but the response we got, like Schilke, was "well he obviously doesn't really want to kill himself" (to be fair, I don't think he really did but he was wretchedly unhappy).
Both times, the first sessions were taken up with family background and child development history. If this is something you don't want to say over the head of your son, then write it all down beforehand and hand it over -- they'll understand and my well be relieved to cut out half the questioning.
Good luck, and do something nice for yourself and your child afterwards. Oh, and try not to blame yourself, as we all tend to, for having a child who needs specialist help (assuming you didn't actually lock your child in the cellar and beat him throughout his early years!).