Yes you can request your notes, but tbh, you couldn't really diagnose it yourselves. You'd need a referral.
My son is under the royal national orthopaedic hospital. He had an x-ray after birth to rule out a broken collar bone and later had tests which involved, basically, running electricity through him (don't panic, it doesn't hurt really and it causes no problems and it is invaluable in determining the level of damage to their nerves - in ds case - severe) and he's had 2 operations but they say there's no point doing any more (unless some damage occurs) because he's regained all the function he's ever going to have.
He functions, but his arm is permanantly damamged. Mostly he's found other ways to do stuff, he's adapted. There are things he cannot and never will be able to do, - like play rugby or bat for England or lift a box down from over his head but he's got good hand function.
In my experience, many doctors dismiss parental concerns, so don't be surprised if the instant reaction is along the lines of go away and don't be silly . Now, I am not saying at all, that your son has erbs - I can't possibly diagnose that and I don't want to come across like I am trying to - but, from your description, I really think it is something you need to have ruled out by tests, and not by the doctor telling you they don't need to look into it
Do let me know how you get on, won't you?