hey themonster (((( hugs ))))
a question, why do u want to take such drastic steps in ur friendship?
maybe what you could do is, get help for yourself, try to actually help yourself alongside... she may see you taking her advice n trying to do better, n that may help her know what to talk n how to help u more too....
Also, what she said, about "if anything happened....." doesn't mean that is the only reason she cares about you and wants to help. That is just a part of friendship as well. Try not to linger on that statement n overthink it.
Question is, Right now, are you there for her? you could ask her n talk to her about her needs, esp considering she is almost/has just lost her pet... you could try being there fr her th way she has been fr u? instead of planning to stop communication i guess...
I suggest, call your t, or pick up his call next when he calls, make an apt. May be a start to being able to help yourself, and maybe also keep your friendship alive.
You are awesome, themonster
Try to see that in yourself as well, be kind n nicer to your self.

SE