Yes, she does need help. I can’t give you a diagnosis on the basis of such little information. However, since she is taking a medication, she is probably being treated by someone. Unfortunately, it looks like she needs more help than she is getting. Sadly, I suspect that she will not respond well if you suggest to her that she does need to see her doctor. She is looking at the world through a lens of fear.
You’ve taken her seriously and made sure that her accusations are irrational. She doesn’t accept the proof you have offered her. Therefore, It is unlikely there is anything further you can do to reassure her that she is safe. If you try to be more helpful, you may find that she will add you to the list of people who are hurting her. If your other tenant were to leave, it is likely she would shift her complaints to anyone new who moves in. She can’t help it. She’s ill. But that doesn’t make her unaccountable for her behavior.
Although it’s good of you to be so concerned about her, you are her landlord; not her friend, not her husband, not a relative. The line between being compassionate toward her and being a responsible landlord for your other tenant is a difficult one. Complicating things further is the fact that you are also under stress because you live there as well.
I suggest you contact a landlord/tenant attorney about how to draw appropriate boundaries with her for yourself and the other tenant. The attorney can advise you on how to protect both you and the other tenant from accusations and, if necessary, how to move her out.
One way to provide some support for her is to do some homework. Do look for resources in your community that may be able to provide her with supportive services or housing. Then check with the attorney about whether it is wise for you to present her with options if living at your place isn’t tenable.
I wish you well.