So basically there is a way out, but it does not involve making your mom understand that you are in danger. No words can make her understand since she did not understand even after three emergency hospitalizations. So you should stop attempting to make her understand because those attempts would be futile.

A more important question is why the inpatient drs did not file a motion to court to override your mom's failure to give consent since you were in danger and they should have done so.

Your mom is neglecting you and in theory, you could call the child protective services and have then intervene and they would know, I am sure, about the procedure of obtaining a court order overriding her refusal to give consent. If you want to go that route, call them now - they work 24/7. If you do not want to go that route but want to petition the court on your own, then we will need to do some additional research.