It sounds like you felt very overwhelmed and you were not able to vent as you needed to. The situation with your daughter became the last straw and you broke down. It happens to everyone. So feeling bad about it is ok, but realize that everyone has their breaking point and that this is normal.
When you look at what happened to you leading up to you lashing out, there is a very clear pattern of very stressful incidents occurring all at the same time. You had a stressful session with your therapist, you had bad news from your doctor, then you saw your attacker in a place you did not expect. These are tough individually to deal with but to have them happen all together is extremely stressful. Couple that with no place to vent your feelings and you have your outburst.
First, realize that you are human. It happens like this to everyone. Then do what you can to repair it. You already apologized, which is great. Talking to your daughter about what happened (screening out the most traumatizing parts) is a good option too. The more she understands why you felt the way you did, the better. Then allow yourself to let it go. Your daughter was raised by a loving mother who has done a fantastic job being a single parent in a very difficult situation. Your daughter is just fine. She understands and will forgive you. Allow yourself to make mistakes and give yourself permission to be like everyone else who has done this too.