Did I do something wrong 😕

Hello. This is kind of a petty situation but I don’t have anyone to really bring it to soooo here we are lol. So my bday was last week and I scheduled a hair appt for myself a month in advance before my bday since I knew I was going on a trip. So this appt has been scheduled since May. The girl who I booked with has a booking site so I booked there. I booked for a June appointment at 2:30 pm which was convenient for me since I got off work at 1 and she was right down the street from my job. Maybe a week after I booked I noticed in my email that she changed my Appointment time to 3:00 pm. No big deal. But I did text her personally just to confirm that she wanted me to show at 3pm instead of 2:30 and she confirmed that 3pm was correct. I agreed! Now I do feel it was a bit unprofessional for her to move my time without asking if I was ok with it first. But then I know some people move things around on their booking sites to open up more appointments without changing your scheduled appt. which is why I confirmed that she actually wanted me to show at 3 and not 2:30. Anyway, I also wanted to mention that on her site it doesn’t give a heads up to constantly check your email for updates or changes on your appointment. I feel that this should be a disclaimer if you solely are gonna communicate with your clients via email. I also want to mention that I had been communicating with her through text too about the kind of hair I had gotten, etc etc. Anyway, on the day on my appt I headed out at a reasonable time so I could make it to her at 3pm. She calls and says where am I and that if I’m 10 minutes late it’s a $20 late fee. So I’m like wait what? My appt is at 3. She says no it’s at 2:30. I said no you literally moved me appt to 3 and we confirmed it via text message. She says if you check your email you’d see that I moved it back to 2:30. Mind you, she never asked me if that was ok to do nor did she mention it to me out of the few times we texted. So I told her I wasn’t open to paying an extra fee and I’d like my deposit back for the service. She refused to refund me as deposits are “nonrefundable” but I’m thinking of making a claim to my bank to dispute this as I didn’t receive the service because of HER mistake. Do you all think the dispute would work in my favor? And was I wrong or should she have communicated a little better?