My mom also worked until just a few weeks before her death from brain cancer. She chose to do that because she loved her work. So add me to the list of people that think it is ok for you to share whatever you need to share with T.

As far as advice: there just is no great way to get through this. You will grieve, and grief is painful. I am sorry. Your grief honors her, in a way. It speaks of the depth of your relationship and how important she is to you.