I'm so sorry to hear this. Prayers and thoughts for you and your family! When she is no longer in the mental health institution I'd recommend finding a therapist that specializes in types of therapy like Trauma focused cognitive behavioral therapy (TF-CBT) and/or dialectic behavioral therapy (DBT) and having weekly appointments. You can also look at doing something called Intensive in home services which will be therapy like 3 times a week for 3 hours. They typically so have a crisis phone you can call at any time. Since she is so young, like you said, they likely can't do many tests, but at this point you don't have to unpack what is causing it you can start to treat the "symptoms" per se. Sometimes we don't really know what causes mental health problems we just diagnose it and then use therapy to treat described symptoms.
Also, it's definitely OK to cry, be hurt, upset, confused, and scared. Pushing down these emotions won't help, but it's also important to not let those responses take control. Somehow you need to find a balance between feeling your emotions and progressing towards healing. Maybe try writing your feelings down and getting all of it out or talking to someone (even if it's not a professional) just to have support. Find things that help you feel happy and make sure you do those a few times a day and as my professor would say "don't should on yourself" meaning don't say I should be strong, I shouldn't cry, I should be doing better. I'd say instead let yourself be sad but after some time try to pick yourself up by those positive things that make you feel better. I hope this is helpful and that you can find a way to move forward!