This... could really be soft Y T A but I'm going to say soft NTA, because I do think you truly considered her wish and sought advice from a hair dresser, and I don't really have a problem with your reaction after the incident -- it was the truth and it wasn't demeaning. I think you should have shown your daughter the preview on the app, though, and let her make her own decision from there, regardless of anyone else's opinion, including yours. Or had your cousin explain it to her, instead of what reads like you making a unilateral decision about her appearance, and go from there. Teach your kid how to gather information, like what you did to draw your own conclusion, because that's a skill she needs to develop.

She's old enough to make calls about her appearance -- good or bad -- that aren't permanent and don't cost you a ton to upkeep, unless you're willing to foot that bill; your job is just to help her learn how to use judgment in a space that is safe to make mistakes and learn. I don't think your reaction after she did the hair butchery was cold and I completely understand your disquiet that she was propelled by social media influence, to the point that she hid to do it -- the fact that she hid is very telling, though, and her pleading with you to fix it says something, too. She's still obviously a child needing guidance and reassurance. Include her more, at the very least, if you aren't going to give her final say or this could set a very bad precedent.

Hindsight is 20-20 and what you did do was technically fine; there are some things that you definitely could do better but I don't think you did anything really, very bad, either. Remind her that hair grows back and see if she wants to try some clips, barrettes or hats for now; and let her have more agency in the future.