Thanks everyone for your responses! I think what has helped me to deal with it the way I have is that I already knew that it wouldn't be best for T be my only emotional support. If she had obliged and hugged me it would have been very easy to become dependant on T and further neglect my personal relationships instead of building on them.

Don't get me wrong, there is still that little voice that is saying "T regected you, she doesn't like you" but I am learning not to pay attention to unhelpful thoughts. It also helps that common sense tells me that statement is completely false.