Le sigh. This brings back such (unhappy) memories of my late teens and early twenties...I feel your pain.
All I can say is this: There have been people who I dearly loved and who's friendship I was deeply invested in who at one point or another "freaked out" on me for (to this day) reasons that aren't entirely clear/don't make sense to me. And we went our separate ways. And it sucked. There have also been people who were deeply invested in ME as a friend, who I liked for a while but for a variety of reasons made me angry/lost my trust/were too selfish/judgmental for me. Being young at the time I "ghosted" them or blocked them, rather than just straight up telling them what I was feeling. So I have both been the do-er and the do-ee (?) of ending friendships. I did have a close friend in high school who "broke up" with me who later told me she'd been struggling with severe depression at the time...it took seven years to go by, but we're friends again, though not like we were. So sometimes people will come around and realize that they made mistakes, and if you're willing to forgive then you can move on. However, it sounds like you're her little punching bag right now, and that's not healthy for you. It sucks her kitty is sick, but that's not your fault or your problem to fix. Let her work out her problems, tell her you'd like to be friends (if that's even still the case) but that her reaction (avoid "overreaction" since that will PO her more) was hurtful so you'll give her space until she seeks you out (and apologizes). But don't place too much hope on reconciliation. Once people reach a breaking point in a friendship, it's often hard to repair the damage, even if both sides want it (and usually, one or both sides don't).