Yeah, I’m going with @augustlan‘s “assumed I am”:
”[I am w]ith my mom [, ] having a breast biopsy…”
or
”[I am w]ith my mom [, who is] having a breast biopsy…”
It’s a poorly crafted sentence because of the ambiguity and because of the lazy way of leaving out the first person and verb. (It’s not like the understood “you” in an imperative sentence: “Close that door!” “Go to the hospital and visit your mother!”) Maybe some day, given trends in language and writing, it will be, but by gawd… not there yet!
Maybe you saw what I did there.
My best wishes to your correspondent, however. Someone’s in fear and uncertainty, clearly. That’s not ambiguous.