As an adult on the Autism spectrum, I can relate to your daughter well. I am glad you got a diagnosis.
the "stimming" or repetitive movements of flapping her hands is common as well as several other traits you mentioned.
Hypersensitivity to stimuli is absolutely an autistic trait. the not wanting shoes, anything on her feet is one of them
mentioning she, like me loves to hug and be hugged. Its what we call deep body pressure. I love it and have to always have it.. I kicked Prozac after replacing it with my collars that I wear all the time ( also happen to the Siberian tiger Therian and a furry) hence how I discovered my collars. its very calming and comforting for me to have a constant pressure around my neck. I also have weighted blankets to sleep with, Tight fitting clothes help too... as a baby my parents had to strap me down in my crib or physically hold me down to get me to sleep. They actually make weighted tight fitting vests (for kids mostly) that have a similar effect. the tighter I am hugged, wrapped, strapped etc the more calm and relaxed I feel. ( there are also Autistics who are total opposite of this)
My suggestion is to try various things such as weighted blankets. when she has a meltdown (temper tantrum) try just wrapping or hugging her very tightly. see if you notice any improvement such as quicker calming, less severe meltdown or shorter time spans etc... You need to find what sensory method meets her need and then take advantage of that to help calm her.
Are you using Hearing Aids with your daughter? if so you might want to try skipping the HA for a while. I have Bilateral CI's and never use them because I figured out that I am hypersensitive to sound. especially sound that does not sound "normal" I had a progressive hearing loss so I know what sounds "natural or normal" and CI is not it.
self play as opposed to social play is also common, I never played with my sister who is 2 yrs older we would just fight. I spent countless days just playing Lego as a kid... We just don't have a need or want to be social esp as a child. we might develop one or two special friends but don't expect us to hang out with every kid in the class.
Language delay, late walking, potty training are also common to ASD. also realize the Autism is a spectrum and ranges from very low functioning to extremely intelligent but still socially awkward.
If she doesn't have any special interests she will develop them. (these are what interests us. We do these activities obsessively and can talk about them for ever and never get bored of the subject. though we will not notice or understand why others become bored when we are doing or discussing our special interests.
on the flip side, Autistic kids will have zero patience for anything that is not of interest to them. (adults too but we have learned to fake it). so it will be in your best interest to find out what interests your daughter and support those interests.
MOST IMPORTANTLY, DON'T TRY AND FORCE YOUR DAUGHTER AND US IN GENERAL TO BE "NORMAL" OUR BRAINS ARE WIRED DIFFERENTLY AND WE FUNCTION AND INTERACT WITH OUR ENVIRONMENT A LITTLE DIFFERENTLY TOO. We are not second class citizens and we are NOT a fricken' puzzle we are People! Autism Speaks is like the AG Bell association of Autism. they want to cure something that is not ill and force us to be normal and hide our real selves to make NeuroTypical (NT or normal) people feel more comfortable. often using painful and oppressive methods.. You are Deaf, does this sound familiar? its should, Audists have been trying to do this to us Deaf for centuries!!! a much better group is
Autistic Self Advocacy Network | Nothing About Us Without Us Autistic Self Advocacy Network: whose slogan should be a familiar concept to Deafies. " Nothing about us, without us!"
here is a great book that I recommend you order, its written to explain Autism and Asperger's to kids but really makes sense for any NT person who reads it. it will help your son understand his sister better. See how many of the pages match your experience with your daughter..
[ame="http://www.amazon.com/All-Cats-Have-Asperger-Syndrome/dp/1843104814/ref=sr_1_1?s=books&ie=UTF8&qid=1369145216&sr=1-1&keywords=all+cats+have+asperger+syndrome"]All Cats Have Asperger Syndrome: Kathy Hoopmann: 9781843104810: Amazon.com: Books[/ame]
Plus you will understand why I have a soul of a Tiger. So having Asperger's is totally normal for me. BTW I had got nickname "That'sCat" Around 10 yrs old from my scoutmaster. who knew how appropriate it was. But I also got it cuz of my behavior and personality.
Oh and you are thinking now.. Wow Southpaw, that is kind of personal and embarrassing to share on a public forum. the answer is No its not embarrassing if you are autistic. Yes it is personal, its about me and i know me very well, we don't really do embarrassed. we talk about facts, reason, science, our special interest because its who we are and what we know. Though I do embarrass my wife regularly by being so, well, by being ME! (the page in the book i mentioned above that talks about us embarrassing friends and family made my wife laugh more than any other in the book)
We learn to adapt and function in the NT world the same way Deaf learn to adapt and function in a Hearing world. Honestly it does not matter if, when you get a diagnosis formally. and often a formal diagnosis will not be given until after the child starts school and extensive social interaction with peers can be observed.
You are free to PM me and I would be happy to VP with you if you want to talk more...
Mew!
Soutthpaw