As Argo puts it, there is no competition between your t and your family. The goal for all parties involved (you, t, family) is for you to get better so they are trusting you to do what you need to do to feel better. If part of that includes talking to your mom, I see that as a good thing especially since your t was unavailable.

You were practicing good self-care measures by reaching out to your mom. I honestly think your t would be proud of you for doing so!

It sounds like you are in a very difficult situation right now, struggling with so much. I imagine the last thing your t or family members want to see you dealing with is the unnecessary added burden of guilt. You did the right thing. You did not displease anyone. Keep doing what you need to do, because in the end, this fight is all about you.