HI and welcome! Don't expect that the poeple you have seen will pick up Aspergers (an autism spectrum disorder). It is missed in girl a huge amount of the time. Girls do NOT show it as clearly and and typically as boys, largely because they mimic what other kids are doing even when they don't know what the social rules are (at least that is the big reason in my opinion). The hair washing could be another symptom. She may have sensory integration disorder, where her brain does not handle sensory input appropriately. Most of us with Sensory Integration Disorder (SID) cannot handle certain things and seek out other sensations. Years ago I attended a very large Aspie support group in the city where we lived. Many of the parents said that hair washing was a big sensory problem for one reason or another. One mother had a 30+ yo daughter and she just washed her daughter's hair for her. The woman simply could not handle either the slimy feel of shampoo or the feel of wet hair on her hands and back. For them it simply was not something the daughter could overcome or handle, so the parents accepted that she needed help.
You will likely have the best luck finding someone familiar with Aspergers to evaluate her. Many of us recommend evaluation by a neuropsychologist. They are psychologists specially trained in how the brain works. You can find htem at Chidlren's and major university hospitals.
It sounds like she may need more than 1 antidepressant (ad). My son is on 3, and needs them all. Strattera is used for adhd, but still is an ad. Trazodone is generally used for sleep problems, and is an older ad. He takes these with luvox - until he was on all three the depression still had a pretty good grip on him. You might ask your psychiatrist about adding a different kind of ad.
Cutting is not something to encourage. It causes a release of endorphins and is addictive. yes, it is not a medication, but it is still addictive just like taking a drug because it causes the same release of endorphins. It is also a sign of deep emotional pain. I don't know the best way to handle it. For some, xanax is VERY effective. It isn't the benzo most docs reach for first for a teen, but benzos can be very very useful. They are more than just straight sedatives. Sedatives just make you go to sleep. Benzos also relax muscles, and they work on anxiety. I don't know if your daughter needs one, but you want to address cutting ASAP with ALL of the people working with her. My mother cuts and has done it since her teens. She hid it until I found signs of it that she couldn't explain away. I wasn't angry, just very worried. Amazingly, she and my son made a pact that neither of them would cut. When they see that the other one is hurting, the reminder that "if you cut then I can cut too" seems to work for both of them.
I am not sure that allowing the hoodies all the time is helpful to your daughter. Forcing her to dress a certain way isn't helpful, but you don't have to allow everything either. For us, the emo look fed into the problems. If the weather is warm and all she will wear are long pants and hoodies, it is a real sign of problems. Often kids dress this way to hide serious cuts. IF they don't have them, it can let them think of those covered parts as areas they can cut if and when they want to. We finally allowed Wiz to wear all the black he wanted, as long as the shirts were not disgusting and the sayings were funny rather than dark or gross or used bad language. In summer he had to wear shorts and short sleeves. In winter he could wear shorts if he wanted to, but he had to wear long sleeves (He is perpetually hot, NEVER wore a winter coat with-o a fight.) If your daughter is hiding in hoodies and tshirts in the summer it is a sign of problems, in my opinion.
My position on the clothes came about because the clothing seemed to feed the depression and cutting and other ways of self harming. I never wanted to battle over clothes. As long as they "cover your Bs" (cover all body parts that can be expressed with a word starting with B), I never wanted to care. With Wiz I HAD to get involved because it became very clear that certain ways that he dressed fed the negativity and self harming. Other than that, I would never have said much. With my daughter the only times I comment are when it doesn't adequately cover her "B's" or when she asks.
As for turning in assignments, it seems to be a problem for a LOT of parents. My dad taught jr high for over 35 yrs, and the last five or ten it seemed like not turning in assignments was the "cool" thing to do. It was something a whole lot of kids did, even if they had worked hard to finish the work!!! Communication between you and the school is important. Many of us have had to take a different approach. For us the school problems and battles over school problems took over life out of school. It seemed all the family time was spent punishing or yelling or following through with consequences for things that happened at school. So we told school, and our child, that school issues were to be handled by the school. If homework wasn't done we would NOT fight zeros and other consequences that were given AT SCHOOL. As parents, nothing we did was making a difference and we had to step out of the problem because our family time was as important as school time. We didn't ask if homework was done. If help was asked for by our child, we gave it of course. but we didn't look to see if assignments were turned in or done at all. We didn't fuss if our kids flunked, or passed. It was up to the child. Some kids realized they wanted to pass and that the refusal wasn't as satisfying if there was no battle, so they started doing the work. Others got in school suspensions and other consequences for not turning in assignments. But our homes stopped being a homeowrk war zone, and we became a family again.
I hope something I have said helps. I am happy to meet you, and sorry you needed to find us.