Your young lady could have a number of things. Certainly it sounds like she does have Sensory Processing Disorder/Dysfunction, and should see an OT for sensory therapy.
She may have an autism-spectrum disorder, or it may be something else. You really do need to see a pediatric neuropsychologist to pinpoint her specific neurology.
When he was little, my son presented to non-specialists as on the autistic spectrum (hyper-focused on specific interests, severe sensory issues, motor delays, inattentiveness in school, delayed development of early milestones such as walking, etc.). However, when he was 7, a pediatric neuropsychologist ruled out autism (the physical wiring), warned us that it was probably neurochemical, and told us what symptoms to be alert for.
He is now 12, has had repeated confirmations through formal testing of high-average intelligence, and is diagnosed with inattentive ADHD, psychotic disorder NOS (hallucinations), and OCD, all of which are under reasonable control with medications. Due to severe dyslexia, he also is delayed in reading skills, and he is using technology (keyboard, CoWriter) to bypass his severe motor skills issues. He currently recieves psych counseling (both in the schools and private), OT, PT, and is receiving full-day special education supports.
You really do need to see a pediatric neuropsychologist to ensure an accurate diagnosis.
If your young lady IS on the autistic spectrum, be aware of the benefits, not just the drawbacks. Autistics are meticulous, highly focused people, who can be very successful in certain career areas as adults, if they have had proper supports during childhood. Unfortunately, "normal" schooling is very detrimental, unless the teachers are motivated and well educated in autistic concerns. Be a strong advocate for your child, believe in her, and be an integral part in selecting her programming. There are several successful programs out there, all involving highly structured environments and predictability.