my 6 year old ***** thumb, doesn't concentrate, teacher says she's tired all the time

My 6 year old still ***** her thumb excessively. When she ***** her thumb she goes off into her own world, and her teacher reports she is tired all the time and can't concentrate.
She sleeps 12 hours a night with no sleep problems.
She is full of energy at home - she never sits down and ***** her thumb or seems tired  - she is always on the go, but she does suck thumb walking along, and would have it in her mouth permanently if I let her.
When she wants to, she can concentrate really well - at home she writes songs and plays that are excellent - but ask her to lay the table  -and you'll never find the cutlery again - she gets distracted walking between the kitchen and dining room.
I wonder if she has too many distractions at school to be able to concentrate, and I wonder if I should have her assessed for a behaviour problem, so she can get help. I am concerned about having a diagnosis or label, and of medication, and would like some practical help.
There are no behaviour issues at school, except concentration and inability to finnish a task, but there are at home.
She never sits still.
She has to be reminded of behaviour constantly when we go out, will go wrong way up escalator, climb on clothes rails, hide under shelves in shops, touch things she shouldn't.She seems to lack self control, and seems to be unable to follow rules, even when constantly repeated - and she has clear boundaries of acceptable behaviour -  like don't jump on the sofa, example of very simple house rule she is unable to follow - there are many more examples!
we have a very set routine for morning, she has been going to school for 3 years, and she seems unable to think that after breakfast she brushes teeth and gets dressed, she has to be asked over and over to get dressed, then has a tantrum because her sister has time to play before school an she doesn't - but she has rushed from breakfast as fast as she can to get dressed and ready for school so she can play, My eldest doesn't seem to be programmed to think x follows y follows z, no matter how much routine is repeated she has to be constantly reminded what to do next.
She has always been clumsy and un-coordinated, and can just about catch a ball, but can't hit it with a bat.
She doesn't comprehend there will be consequences to behaviour - that good behaviour will be rewarded, and bad behaviour punished, she has temper tantrums,slams doors, hits her sister.
She blames everyone and anything else for her behaviour -never accepts anything is her fault.
She has to be warned before going anywhere or leaving anywhere, or she can get hysterical.
She is very disorganised, and won't tidy any toys away unless told, and then she always cries and asks for help as she doesn't know how to do it on her own.
She sometimes cries hysterically when disciplined, but says her brain won't let her stay sorry, and she hits her head saying her brain won't let the words out.
She says she knows how to behave but her brain doesn't, and her brain tells her to do things, and she just does them.
She is a bright, bubbly, lovable, sociable child, full of fun and laughter, she got friendship award this year, for being so friendly to her classmates. She loves art and is incredibly imaginitive and creative, she is average with reading and writing and needs no special help at school, she enjoys school, she is always eager to do home work.
When she is good she is very very good, when her behaviour is bad she is exhausting.
We don't smack her,  and shouting is futile, we use time out and toy confiscation, and we use reward charts. Whether reward or punishment, she says she doesn't care and likes being naughty, and she doesn't like being praised! how do we deal with this? it can take her days to snap out of the behaviour and back to her happy self, but is still unable to accept she was at fault (we don't force this, but my youngest child says sorry immediately, and is remorseful, and tries to make amends etc... just comes naturally to her on the rare occasion she does anything to be sorry for.. but is not forthcoming from the eldest)
She has a very stable home, myself or her dad take and collect her from school every day, she has a very tolerant 4 year old sister who has none of the above behaviour problems.

[specialmom]

Please google sensory integration disorder as you describe it to a T with your daughter.  My son also has sensory integration disorder and was diagnosed at 4.  He is now 6 and in kindergarten and doing really well after addressing his sensory system.  Sensory Integration disorder involves the nervous system and how it regulates and processes things in from a child's enviroment.  This can involve so many areas.  I'll touch on some things that you said.  Your daughter is different at home than at school.  This is common with sensory in that a child's nervous system is flooded when they are out of their common enviroment or feel overwhelmed out out of control. School does the same thing to my son.  A child that is acting tired, floppy and inattentive in school has an engine that is running too  low.  She is not getting the input her body needs to "wake up".  When she is bouncing off the walls and concentrate when she is in this state, her engine is too high.  Her goal (and yours) is for her to be "just right".  Touching things is the brain craving input about the item . . . she's just gotta touch it.  She lacks impulse control to stop herself.  This comes deep within so following a rule is very difficult.  Tripping was one of the first things that was brought to my attention regarding my son.  Motor planning is the part of the system that controls motor functioning.  Does she sometimes shy away from new things like pedaling her bike the first few times?  How is her handwriting? Tantrums with a sensory child can be monumental-------  way over the top and takes a long time to calm down. This is due to regulation/modulation of the nervous system.  Self soothing is hard and I suspect your daughter will suck her thumb to  calm herself or when she is bored.  My son chews his shirt sleeve.  
An occupational therapist evaluates for sensory integration disorder and does therapy for it.  It is play therapy and behavioral modification thrown in.  But it directly works on the nervous system.  For example, before school---------  if you had a mini trampoline (we got one from K mart for 30 bucks)-------  she could jump on it to wake herself up before school and give some input that she wants.  You could then do a game of animal walks---------  including the crab walk, bear walk and leap frog among others (make it a game and make it fun!).  She can be your "helper" and carry a bag of heavy books across the room.  Give her a thick piece of chewing gum before she gets on the bus or during the drive to school. Make some of these sensory strategies part of every morning to help her get regulated before school.  After school, a trip to the park in which she runs, climbs, jumps, swings, rolls, etc. is all very good for the nervous system.  Swim lessons are excellent(deep pressure and "heavy work").  Gymnastics or tumbling would be great or soccer.  All of these activities will give much needed input to the nervous system.  
"The Out of Sync Child" by Ayers is a good book but to be honest, I found out the most information from the internet.  I have a million strategies for behavior, following directions, and things that help the nervous system to stay regulated.  Google sensory and tell me if you are interested in some of that info and ideas.  As I said, my son was diagnosed at 4 and is really doing well.  He only had one bad episode the entire school year!  It's been hard work but well worth it and I'm happy to help any other families that need it.  I also could be way off base here .  .  .  but feel like sensory is an issue for your dear daughter.  I wish you luck and please let me know if I can help!!