Yes--I agree with other posters.
You need to level with her that this is already causing you health issues.
You are quite right that getting her out after the two months may prove impossible if she refuses, is drinking, and hasn't found another situation.
I think you should offer her what "up front" help you can for her finding her own place and keep her out of your home.
That's your refuge--don't risk it.
Welcome to SR and I'm sorry you are dealing with such a tough situation