You are certainly not being unreasonable. Take the space and time you need now to self-care. Even when you are caught up on doing that, it would be very appropriate to back her off with some boundary setting. Her threats of self-harm or suicide are a form of emotional blackmail: "Soothe me or I'll harm myself, and that will be on your head!" Do not believe that garbage. She deserves compassion, as we all do. But it is her responsibility to manage her mental illness. You will not be doing her a favor by enabling her excess neediness.

Down the line, you might consider calling her bluff. You could call 911 in her area and request that police do a wellness check. If you have more time and energy, you could say, "Would you like me to drive you to the ER at the hospital, so you can be assessed by a clinical social worker? Perhaps, you need to be admitted to a psych unit." If she ever says "yes," keep in mind that she will probably be made to sit and wait for a long time at the hospital or psych emergency facility before they give her attention. If you bring someone to the ER, don't agree to leave, if she gets bored and tired. One trip like that will probably discourage her from wanting a repeat visit.

I agree with @tart_Cherry_Jam. She is an emotional parasite. No doubt, she does experience genuine distress. But adults are supposed to be capable of self-soothing to some extent. Even children have to learn that. Even kids cannot expect to be catered to everytime they have an episode of insecurity. A child who gets that all the time becomes addicted to instant and constant reassurance. They become emotionally dependent. Maybe that's what happened to her as a child. Or maybe she was deprived of a reasonable amount of reassurance, which all children are entitled to. I don't believe in leaving babies to cry. I do believe in being very attentive to young children. However, at some point a child has to be weened emotionally, as well as physically. It might be interesting to try and figure out how she became this dependent. She didn't get that way all by herself.

Sometimes it can be helpful to give a needy person something to look forward to: Like, "I can't talk (or text or email) to you for much longer this evening, but I will touch base with you tomorrow at noon to see how you're doing." Good luck. Needy people can be very persistant. You have to draw the line somewhere and stand your ground.