Does she have any issues with concentration? She sounds a little ADD and if she is or might be, there are techniques that might help her with organization.
I think your biggest issue is getting her buy-in. I would sit down with her to ask her how it feels to have a morning like she just had, to not have what she needs, to feel worried about missing an appointment, etc. Ask her if the anxiety is worth doing everything herself. Then offer to help her keep on top of things. Remind her that it takes 30 days for an adult to create a habit and that if she reinforces the counterproductive habits, like forgetting to wash clothes or set an alarm, that what she will learn is how to forget. Remind her that it is your job to help teach her the skills she will need when she's fully grown and on her own. Remind her, too, that no one truly does EVERYTHING for themselves all the time. You and your husband may split duties, you may have a friend help watch the kids so you can go to the doctor, at work people have coworkers and assistants, and there is an entire market out there of productivity tools, including Blackberries, to help people get and stay organized. Very few people can do it on their own and there's nothing wrong with asking for help.
The flip side, of course, is that ultimately, she is responsible for getting her act together and there are logical consequences for not following through. Let her experience them. Be empathetic but don't recriminate. Ask her how it feels and ask her what she could have done differently to bring about a different outcome. Remind her if she needs help, that you are happy to help, but you can't live her life for her and this is the start of the part of her life where she becomes completely accountable for her choices.
If you nag her, lecture her, or otherwise treat her like the child she is, she will continue to play deaf. I doubt it is to truly infuriate you, but at this age, the streak of insecurity and independence is strong, but capability hasn't quite caught up yet. Playing the empathy card and offering without judgment, and without bossing, may find her more receptive. For truly important things, you may have to just deal with her irritation because it is unavoidable.
Perhaps if you instituted some changes as well--a last check before bedtime where you go to each person in the household, without singling anyone out, and say "I am thinking of running a load of laundry, if you need something washed, put it in the laundry basket" it might help her. Is there anything to which she responds particularly well? I am a list maker, but for alarms, I have to use my phone. Some people use a digital device for everything, some people need pen and paper. Maybe the wipe board doesn't work for her, but a weekly printed list might, or something she can hold in her hand, like an engagement calendar (which i also use).
Is she an adult? No, but she's reaching an age where she's starting to grasp adult ideas and have adult desires for herself, to have friends, have fun, look a particular way, and these are all things you should nurture and respect. With boundaries. If something is non-negotiable, that is where you make you make your stand. If you have a family function, or a drop-dead deadline and it is imperative that she be prepared, you have to make sure she does everything, regardless of her attitude. Apologize, say you understand she finds it frustrating, but it's your job to make sure that you get where you're going on time in a certain way and you cannot afford for a single person to not do their tasks. If you were a boss and she were an employee, that's exactly how it would work.
Good luck, this is a tough age. Remember empathy, compassion, and enforcement of non-negotiable boundaries will go a long way. Engaging her in the drama, arguing, recriminations, they will all push her further away.