Your therapist is one of two people that you should tell *everything* to. (The other one being your attorney.) If ever at any point, you don't feel safe disclosing something, then it may be time to get another therapist.

If you had a newborn baby with you, and the baby was hungry in the middle of the session, you wouldn't think twice about feeding the baby while you continue talking. In fact, you'd probably have a bottle ready in advance, rather than just let the baby cry the whole session. Take care of yourself just as lovingly. Have your snacks or juice or whatever you need, right there with you. No therapist of any quality would object to you doing what's necessary for your health.