What’s this “call an ambulance” & “the hospital has to hold her until they can place her” thing all about and where do I sign up?

I’m the only caregiver for my mother and I am very very, dangerously close to losing my mind. She plays helpless invalid and she is NOT either helpless nor an invalid. I was the good daughter for over ten years and it cost me myself my sanity my career my life. I am in a major, dark , hopeless depression and I’d rather be dead than live like this. I cannot get out of bed most days, nor can I motivate myself to gather up the paperwork required to apply for home care or anything. This sucks. Life sucks. I’m trapped in a scenario that sucks. And my give a damn is way beyond repair. I do not know what to do. So, how does this call an ambulance thing work?