I would never do this as a therapist. Sorry, but that was a bad decision on your therapist's part.

First of all, it was not a medical emergency. You have some health issues and you got a recommendation from her to see a specific doctor, that's fine. But there was no need to do it exactly on that day and there was certainly no need for her to take you there. I understand that you don't drive, but you manage your life somehow. I assume, there had never been a need for her to give you a ride before. So why now after the last session?

And, it's completely unacceptable to do this kind of a favor to a client at the expense of another client. If that client knows the real reason why your therapist was late for that session, they have every right to be upset and angry about it.

Also, the last session should have some sense of closure. It's the time to say good bye, basically. Taking a client to some doctor's office and then calling them to ask how it went doesn't create a sense of closure IMO.

Sorry, if this feels like a cold shower. I understand your excitement and I am not blaming you for feeling how you feel. It does feel fantastic to be cared for in such a way by a therapist, so there is nothing wrong with how you feel. But your therapist should've handled the last session differently. She crossed the boundary. Not every boundary crossing is necessarily unethical, and this one was not, but it was definitely a bad judgment.