First, I highly doubt that your younger sister evens remembers this happening.
And, no, you should not be beating yourself up over this. But, the problem is that you are apparently beating yourself up over this!
Anxiety, left untreated is not good...and can lead to depression. And, since the anxiety could also be caused by much more then the event you mentioned, I would recommend finding a doctor (probably a psychologist) and getting help for your anxiety. That doctor could also help you with dealing with the event you mentioned. If it turns out that the single event is what is causing you your anxiety...I think it can be handled fairly quickly. However, I would be somewhat surprised if this one brief event is the only cause. I think it would be worth your time and effort to find out what is going on. Good Luck....and let us know what happens.