It's a beautiful thing, but I understand why you would call it a "weird moment." I have had a similar experience in therapy and it was pretty much too intense for me to handle.
As far as "I am confused by what is happening, who is hurting and whose pain this is and who should be comforting whom."-- It seems as though your therapist was experiencing the deepest level of empathy-- he was truly experiencing
your feelings
with you. It is still your pain, only he is feeling it right along with you so that it hurts him too. And he can feel your hurt so much. When it gets this deep and he is able to reach your feelings on that level, it can seem as though the two of you are are one. In regards to comforting, sometimes if the experience is really intense, it is sometimes okay for the therapist and patient to comfort each other. When I had the analytic couch experience, T seemed to take it even harder than I did. He said that he knew how painful it was for me and it became that painful for him, too. A couple weeks ago when we had revisted this, I told him that even though it was a difficult experience it was so important to me, mostly because of the connection afterwards. T said, "I think we calmed each other down." I'm so happy that this happened for you, Sunny.