I really don't think she will.

Yes!

I think you could say "I am having a really hard time with my health anxiety (if she knows about it), and after our session, I had a panic attack and was in the shower, and I felt at that moment very hopeless. Could we meet next week?"

That way you keep it general, but shows the seriousness of it. If you want, you can say "I felt so hopeless like I wanted to die, but have no intent. I am just scared."