There could be a lot of things going on with her. I would look for a neuropsychologist. They are special and are usually at children's hospitals. They do very in depth testing and often give better answers than regular child psychologists/psychiatrists. It can take months to get in, and you will need a referral from her pediatrician.
She also may have sensory issues. You need an occupational therapist to test for that. Does she seek out or avoid certain things? Is she picky about her food? Does she look for loud noises or avoid them like the plague? Sensory issues can make life very difficult. It often can feel like the world is attacking you on every front. I have my own sensory issues. I am the pickiest eater in my house and I always was. My kids' food preferences and allergies were nothing compared to my pickiness. I cannot wear - or even touch - some fabrics and textures. I can't pull cotton out of a bottle of medicine. It just feels awful to me. I never touch cotton balls. I cannot tolerate loud noises. I don't like a lot of noise. I hate anything electronic that talks to me or beeps at me. Alexa and I are NOT friends, lol. It can be hard to navigate the world when so much of it feels awful to you. I never talked to anyone about most of this until my own kids were being tested for sensory issues. My youngest son used to sit on his head (upside down) to read and watch tv. I just thought he was a weird kid. As long as he kept his feet out of other people's faces, it didn't bother me. That deep pressure on his head was actually a sensation he was drawn to and helped him calm down when overwhelmed. He would get very overwhelmed, to the point he would just stop registering the outside world. This was a problem at school because going to school every day in the very early grades was too much for him. I let school see what he was like when he was overwhelmed and scared his teacher half to death. He crawled under a table and curled up into a ball and wouldn't react to anyone. I was sitting in the car reading a book when they called me. I knew it would happen, and I hated it, but I knew that if school didn't see the problem, we would have attendance issues.
His sensory issues were at the more severe end of the spectrum. Most kids with sensory issues do not react like he did. They are on a spectrum with more and less severe ranges of behavior.
The great thing about sensory issues is that you can do a LOT to help them. Unlike other therapies, the things that will help your child are things they are drawn to. So this was therapy that I didn't have to fight my kids over. The occupational therapist we saw gave me a very long list of toys, art projects, various things that would help my son. We had more than 75% of that list because Grandma and Grandpa always indulged the kids a lot. There is even a therapy that can help the brain process sensory issues better (essentially rewiring how the brain handles sensory input) that does not involve any medication. It is called brushing therapy and it involves going over the body in a specific pattern with a surgical scrub brush (very soft brush with no soap). You then follow it with joint compressions. It really can make a big difference. You MUST be taught this by an occupational therapist because if you brush certain areas you can create real physical problems for the child. It is easy to do, once you know how. And most kids like it.
Schools have occupational therapists who can test your child. I strongly urge you to also get a private evaluation if at all possible. School therapists will test for how the child reacts in school only. Private therapists test for how the child reacts to their entire world, which is very different.
I wasn't always a talker either. I was Chatty Kathy at home, but at school? Not nearly so much. Especially starting around 2nd and 3rd grade. I just didn't understand what the other kids were talking about or why they were interested in certain things. I still have no idea why sports involving balls are entertaining to people. After a while, I got tired of the teasing over various things, so I stopped talking. I went an entire year (5th grade) without talking to much of anyone outside the librarian. I was in a parochial school and flat out refused to talk to the priest. Not even during confession would I talk to him. I had books and generally read and kept to myself. My parents had no idea this was happening. No one from school called them about this. This may be part of what your daughter has going on.
I hope something here is helpful. If you need to know more on sensory issues and Sensory Integration Disorder, the best book I can recommend is The Out of Sync Child by Kranowitz. It really explains sensory issues and how to help them. The same author also wrote The Out of Sync Child Has Fun. It is packed full of activities that help treat whatever specific sensory areas that are helpful. It is one of the most fun and useful books I have ever owned. We wore out copy after copy of it. At one point I swore the neighborhood kids had cameras on us because every single time I got the book out, kids just showed up in our yard, wanting to play. Again, the activities your child would find fun are generally the activities that will help them.