Hi, sorry your having such a hard time of things with your daughter, I know this is all very scary. I don't know much about Asperger's, but I do know self-harm. Your daughter will probably benefit more from a psychiatrist than a psychologist. A pdoc (psychiatrist) has more advanced training for these disorders and is also an M.D. so they can prescribe meds, do blood work or any other labs that might be needed. There are medications that help with the urge to self harm, the main one is Lithium, you might ask your Dr. or if you go to a new pdoc, about the benefits of Lithium for your daughter.
Hang in there, your daughters very lucky to have a mom that cares for her so much.