I had a similar situation in my life the other day FS. I yelled at my own mother to "shut up" very loud and very aggressively. I also agree it is a very hurtful way to shut someone down, and I've never used it in this way before.
Our family was moving a family member to a new space, and moving items in and out of my storage unit. It was cold and dark out and I was lifting an incredibly heavy item through a small door onto the icey driveway into my car. I was trying to concentrate and not hurt myself or the item I was lifting. My mom in her attempt to help was physically in my way, talking over me "can I help? let me get that. Here I'll grab an end". I had already lifted it, so this was in my way and not allowing me the concentration I needed. So I yelled. I immediately (after putting the item down) apologized profusely and hugged her. Told her I had needed a little space, but that I shouldn't have yelled.
It hurts us just as much as it hurts them to realize you did something regrettable and not in character. Forgive yourself. As you said, adults process our friends'/family's mistakes differently than teenagers - thank goodness. So I hope D has had the space she requires and might be open to you talking to her a bit about it.
