Does my child have Aspergers? Is it best to go through school or GP to get diagnosis?

When he was a baby, he would arch his back and scream when picked up. As he moved to toddler age he would scream and headbang on wooden floor, he would be physically aggressive with me and never showed any affection.
I asked for help when he was about two and was told when he starts to attack you or headbang, walk out of the room he wont hurt himself. This worked or so I thought it did but now I think it was more that his speech was developing.
He is the total opposite now he gets frustrated and cries but doesn't tantrum and is very loving. lots of cuddles but no kisses.
He is now six, he makes eye contact with his family but not with outsiders, teachers etc.
He is obssessed with mario and zelda and talks in great depth about them,
He has a restricted diet and different foods must be served on separate plates.
He flaps when frustrated and twirls his fingers and toes when excited
He is very self critical,  needs constant reassurance, cries without tears. For example he will ask for a drink I will say "Please" he will then reply with crying noises and "I am a naughty boy I have no manners you hate me don't you. This is constant all day long. He also asks constantly " I 'm a good boy aren't I?"
He has phobias about buttons, germs and insects.
He struggles with noise complains about clothes, labels hurting him.
He complains of fatigue and pain in his legs and spine if he has to walk for longer than five minutes..
He can repeat entire episodes of tv programmes, he often says random strange things such as "Abortion is murder"
He doesn't seem to be bothered about routine although he would prefer it if he never had to go out of the house.
He is doing well academically at school but has no friends.
He has been referred to OT for his gross motor skills.
I am concerned that because he is so well behaved in school and is doing well academically that they won't push for a dx do you think it would have been better to go to my GP with my concerns?