Hi Wozald1989
I'm the poster Polter was talking about, Having a rubbish social worker is going to make thigns harder for you, as well as it being the school holidays, if it was term time i would have suggested you ask her teacher to writer to your doctor confirming her odd behaviour and lack of social skills.
Be very assertive, GP's seem to be paid to dismiss their patients problems rather than do anything useful, you want a referral. When they refuse, or are about to refuse ask if it's money or funding related, i find it gives them a kick and they seem to want to prove you wrong.
First, Video her when she is displaying the strange behaviour, especially self harming (hitting herself / banging her head against things) this is how i finally convinced my doctor to give My nephew cognitive behaviour therapy. This will give you something to "show" it's not a normal tantrum.
The sleep issues and the Tantrums are the two things a doctor will take notice of, so these are the things which should be emphasised in order to get the ball rolling (for some reason doctors don't seem to care about toileting issues at all, Don't be suprised if the advice for this is to use pullups)
Take her with you when you go, as the speech problem will be more evident if she is there.
Is the doctor likely to have a record of her history, if not you should sit down before hand and make a summery and what you know she has experienced.
Secondly at some point in the future i'd find out about getting another social worker and making a complaint. Don't make it personal, just write to the social worker’s manager and explain how you feel the care of duty has been terrible.
I hope that helps a bit, or at least is useful in some way.