Here is my two cents and a couple of points I want to emphasize.

1. It's not your responsibility to make your T feel better. As a professional, she is in a position to take care of her feelings.

2. As far as I see, there is no reason for you to apologize. You didn't do anything wrong. You honestly told her about your mental state and, if anything, she, as a therapist, should appreciate it.

If I were you I would talk to her about the difference between you feeling SI and wanting to act on your feelings. I would not leave a message about that. This is a kind of conversation that needs to take place in person IMO. Explain to her nicely that you appreciate her concern, but that as long as you are not actively SI she doesn't have to check on you regularly and that it would help you to know that she is ok with your SI feelings as long as those are just feelings. Tell her that if you experience the urge to act on your feelings, you'd contact her and ask for help.

Oftentimes, therapists just need to have a peace of mind and to know that clients will not act on SI feelings and that if the client is in a tough place they won't hesitate to contact T and ask for help.