From what you've written I agree, she shouldn't have said "I'm here"...it didn't mean ANYTHING from my view though, just that she didn't know WHAT to say because she KNEW she wasn't going to say " it's ok, no need to pay me". Kind of like a filler, instead of um or er or plain I don't know what to say. You kind of busted her when you called her insensitive, but I agree with you, she WAS being insensitive as she probably could and should of offered a free visit, but didn't.
IDK, maybe therapists NEVER do free sessions? My H and I were self employed for many, many years and we did plenty of free services for our customers. Especially when payment was a hardship.

I hope you feel better soon! Big hug!