TIFU by crying my eyes out at my nail appointment

Tomorrow is my prom and I wanted to get a set of nails with some butterflies that are a bit difficult to draw and some sparkles. So I made an appointment with the best nail tech in town a month ago for today, at 11:30h, or so I thought. When I came to her salon at 11:20, there was another girl and she told me that she called her since I didn't show up. Btw she sent me a text at 11:15, but I didn't see it in time. My appointment was supposed to be at 11h on the 30th, not at 11.30. I tought it was 11.30 because I asked her if she was availible on the 30. (in my country it's 30. with a dot, not 30th) and she said "yes, is 11h 30. okay?", so I didn't think she would mention the date since i asked specifically for that day. She told me that she will do my nails since I have prom tomorrow, and the other girl was nice and said she wouldn't mind and that I can get a small design on my nails if I want to. Long story short, I got plain pink nails with a couple of metalic sparkles. The nails are okay, but they aren't like I imagined them to be and they don't really go with the dress. But I'm not going to complain, since she was really nice and insisted on drawing at least something even though I told her she didn't have to. I appologised to her and to the girl for the hundredth time, gave her a tip (which isn't mandatory in my country) and basically ran from the store in tears. I also cried during the entire process and couldn't wipe my nose and I don't even want to know how I looked like. She finished in about 45 minutes and had some time left for the other girl, but she had to move the other appointments for about an hour each.

I don't care that much how my nails look, but I feel extremely bad for messing her schedule for today. And I'm also super embarrassed for crying that much. I wanted to do two more sets of nails during the summer but now i don't know if I would have courage to show up just to take my nails off, let alone for correction. And I don't even know wheter she would give me another appointment ever again. I wanted to also send her a message to appologise, but I don't know if that would be too much apologising.

TL;DR: showed up late for a nail appointment because I missread the time and cried the whole time because I felt bad. Now I'm too embarrassed to go back there ever again.

Edit: I just want to thank everyone for heartwarming messages. It means a lot to me, especially since I expected a lot of negative comments because this is such a trivial thing. I am very tankful for your understanding and support and for not judging me. It really means the world to me.