Did they have a valid reason to charge me this or should I call my card provider

Last weekend I booked an appointment to get a facial and eyebrows done, I've gotten my eye brows done before somewhere else so I know you should show up a bit early. I scheduled it for 2 pm and a day before I got a call asking if I could come in at 12pm instead and I said sure. Money is kinda tight but with the month I've been having I needed to treat myself. The night before I ended up staying up 7 am due to my boyfriend having an episode and ended up sleeping past my alarm and appointment. They did charge me the full amount which was $108, I didn't know if I should call my card and have them reverse it or leave it. This isn't a family owned or one girl business, this is a company that has customers in everyday and is constantly making money. I know I should've been there, but I originally asked for a different time and didn't get the service