I was much the same from the age of 7, although I wasn't diagnosed with Asperger's Syndrome until I was 11 (and it was my teacher who first noticed that I was different). I've never liked noisy surroundings and crowded areas, which would either frustrate me or make me really nervous (making me want to just go somewhere away from all the fuss) and often, I'd get so nervous that concentrating on people talking seems almost impossible. I would also start biting my nails (to the point where they'd almost bleed) when I get into situations like that. And I don't think I've ever been comfortable giving people eye contact. But from what I've found out or been told about it, those are just some of the classic signs of Asperger's Syndrome. The one thing about GPs it seems, a lot of the time they don't suggest such conditions unless a: it's highly obvious and/or causes somewhat violent behavioral problems, unexplained mood swings etc. or b: they prefer someone else to suggest the idea first (whether a teacher, parent, etc). At least that's the way it is with many of the GPs I've ever met. Possibly because some parents may be in denial or get angry at such suggestions. So, a GP may notice, but may be worried about saying anything in case you react badly to it. But that doesn't necessarily mean that they can't help you. The best thing to do is to mention your concerns about it and see if they can work on making a diagnosis for your son's condition. And if they simply try to dismiss the suggestion, you can either go and get a second opinion or just keep insisting that they help you and your son (and don't take no for an answer). Sometimes you have to get pushy to get the help you need. Anyway, good luck for you and your son and I hope you get the help you're looking for. =o)
Given the description you’ve provided, I recommend having your son assessed by a professional with experience diagnosing individuals with autism. Pediatricians often have little experience making these diagnoses and are, in most cases, not the best person to be making them. The types of repetitive movements that you describe and toe walking are observed relatively frequently in children with autism diagnoses. A reason why the doctor may not have brought it up is that it sounds like your son is developing well socially and communicatively. Autism diagnoses require an impairment in these areas.
While I recommend having your son assessed, I also recommend seeking treatment for the toe walking and hand flapping regardless of the diagnoses. Find a behavior analyst in your area who has treated behavior of this sort before. For children like your son who don’t have concomitant intellectual delays, these behaviors can be very effectively treated through habit reversal and the arrangement of contingencies to motivate him to attend to what he is doing and stop. You keyed in on the fact that he doesn’t even seem to be aware that he’s engaging in these behaviors. The interventions that are typically effective involve teaching him to notice (perhaps have him even collect some data for himself) and then to do something else when he finds himself doing it. On top of this, favorite games and activities are arranged if he can go for longer and longer periods without toe walking or hand flapping. All-in-all, your son presents as a child for whom interventions of this sort should be very effective.