I'm an anxious person too, so I can identify with many of your daughter's reactions. I too am an oldest child and a people pleaser. My mother took the straightforward approach of listening to me and then telling me the solid facts about whatever I happened to be worrying about. That approach didn't help me much then because I was determined to worry, but it does help me now.
A few suggestions:
1. Make sure your daughter does know the truth. i.e. Make sure she knows that she isn't responsible for making people happy. People are going to feel what they want to feel, and their feelings don't change what sort of person she is or how much she is worth. If she did her best or what she thinks is best, then she has done what is required of her. If she has trouble accepting that, then give her examples from your life or have her repeat the idea back to you.
2. Is she a reader? Does she read above her age level? I was a voracious reader, and my parents pretty much just let me read. That fed my imagination, which contributed to the scope of my worry. Keep an eye on what she reads or watches. Talk to her about it, and if she worries about things that are happening in those books (anything is possible to a worrier), then show her how unlikely those things are in the lives we live here. Scientific evidence is good.
3. Help her remember and focus on the things that she did well and how much they help other people. Worriers tend to forget the good things they do in light of the bad.
4. Look at her work load. Kids these days have a lot of activities and obligations. Does she have a lot of things that she needs to get done? Does she feel like she has a lot of things that rest or rely on her to get done even if they're not really her responsibility? If so, take a few activities off her list or maybe make a rule saying that if she wants to help someone, she has to ask an adult first. People pleasers often take on too much responsibility.
5. Remind her that there are other people who take care of her and of her friends. God watches over all of us and makes sure we all have what we need. Mom and Dad are there to offer advice, to protect and provide. Teachers know what needs to be done in the classroom. Encourage her to believe these things and to look for examples of how they are true. Concrete evidence always helps.
6. Look at your own life. How much do you worry, and how much do you worry in front of her?
Anxiety and confusion often go hand in hand. A person who is scared of doing the wrong thing seems impulsive because they have no confidence in their ability to make a good decision and evaluate the facts, so they strike at random. At least I do. I have also found that worry is kind of exciting (not that I thought about that as a child). It feels real, even though it's only in her head. It ups the adrenaline and feels like caring for a person or doing something important even though it doesn't lead to either one. So
7. Help your daughter learn to relax. Meditation is good. Teach her to sit and think about practical things or happy things or peaceful and reassuring things for a certain period of time. Don't tolerate what ifs or buts during your meditations. Your thoughts have to go in one direction.
These are some things that have helped me as an adult. I would also recommend talking to a therapist (I know a good one if you're interested). Worry can become a habit and needs a lot of work to overcome.