Thank you for taking the time to write about your daughter. While it is not uncommon for 7-year-olds to be lacking in social skills, some of the behaviors you describe (e.g., engaging only in soletary play, skin picking until tissue damage occurs) are seen in some (but not all) children with Aspergers. The first thing I would recommend is to discuss your concerns with your pediatrician. Describe the behaviors that concern you, including her difficulties in school. Ask him or her if there is anyone in your area who specializes in diagnosing children with Aspergers. Also, talk to both your pediatircian and individuals from your daughter's school, and see if there are any board certified behavior analysts in your area who work with children with autism spectrum disorders. Behavior anaysts have successfully developed interventions for children with autism that have improved social skills, play skills, and academic skills.
Best of luck with your daughter.
My son (8 years old) has Sensory Processing Disorder (aka Sensory Integration Disorder)...That could be one of you daughter's issues - socks lined perfectly on toes...doesn't like hugs...