Hi trying my best,
Can I just say I'm in a similar position to you so I understand the strain this is putting you under. The previous person's advice is amazing and so practical. And boy, yes difficult questions, but also very important.
Can I ask if there are wellbeing services run through your university? It is a standard thing these days for universities to offer help, certainly so in the UK. I would say go to them and say you are worried about her because this is a lot of pressure for you to deal with and try to help alone and you need as much as help as you can get (believe me I know!). I don't know if your local NHS crisis team have been helpful, or if you know much about support services in your local area? If you are at any point critically worried at what she might do you can call those services.
Once you have had the conversation with her about getting help, you could offer to go with her to the doctor for support. In my experience the person suffering generally finds it really difficult to communicate with docs who are on time restraints for assessing whether someone gets mental health support.
Finally, you are not to blame for any part of this really difficult situation. It sounds like you're trying to be really strong for her and it's a very steep learning curve supporting someone through suicidal feelings and attempts, so try to be kind to yourself.
I hope that helps.