Moonkin, it's OK. Don't beat yourself up about it. I think it is a good opportunity for you to learn that when T doesn't answer your emails, it could be something totally unrelated to you (she is injured, out of town, busy with her family, etc.)
I am reading this little book right now called
The Four Agreements, and it contains 4 agreements or principles for living one's life. One of them is don't take stuff personally. I find I do that way too often, and I see that in your misunderstanding about why T wasn't answering your emails--you were taking it personally and it had nothing to do with you. This little book is kind of pop psych/philosophy, and I don't agree with everything in it, but it has some good parts that I am learning from!