What you did was not terrible at all, but perfectly natural. I've googled my first therapist to kingdom come, including Facebook pages of his family, and at times it has caused me considerable pain. I hope you are able to put the guilt feelings aside as I have, because it is a natural part of attachment and desiring closeness. It's scary and confusing to find the information we're looking for.
Try to remember that your T cares for you uniquely. She knows you and you know her in a way that her children are not part of. Although she is not your actual mother you share a relationship that has been healing for you, and in the cold light of day, whatever other relationships she has don't change the special relationship you share. This may take a period of readjustment in the relationship and some processing. The time might be right to discuss the transference with her. I do hope you can contact her before the next session.
Please keep yourself safe tonight, and draw on whatever resources you need (internal or external) to ensure you are safe. You will get through this, and it may strengthen your relationship with T in ways you don't expect.