I had 3 of these! And I survived; and they have become charming young women.
She doesn't get it at all - she does, but she cannot back down and lose face.
I would suggest that you made too much of this. Maybe just say "Oh - that's a shame - it would have been a help if you had done X" - then move on. The mistake you made was to get embroiled in it - once you do that it all spirals out of control and becomes something bigger than it really is. You say things you wish you had not; and she does the same. It has spiralled into personal resentments and loss of faith in her essential goodness.
She doesn't care that she's really upset me - she does; of course she does, but she cannot let on. She is trying to move away from you and become her own person, and she is doing it in a ham-fisted way. She is preparing to move from being a child, who does as she is told, towards being an adult, who makes their own decisions. She does not know how to navigate this journey - she has never done it before. And there will be other things in her life which will make her edgy - maybe there is a boy she fancies and she does not know how to handle this; or she has fallen out with a friend; or she has seen something online that has worried her. Lots of possibilities.
I would counsel you to pick your battles. Honestly - saying that she did not do something you wanted her to do is a mere nothing. Save the arguments for the big things - drugs, inappropriate relationships, getting drunk, accepting lifts with drunk schoolmates, staying out very late etc. etc.
Go and talk to her - tell her you over-reacted - tell her you know she is great really - tell her you love her. Then move on.
There will be plenty of battles to come and she needs you to not become upset, but to be the strong adult who never loses faith in her. I let a lot of things wash by me and concentrated on the things that really matter: that they knew I loved them and that I recognised that things must change in order for them to grow up.
There are positives - watching a young girl turn into a young woman is exciting, but challenging.
Good luck with all this.