Am I being unreasonable for thinking I’m being overcharged at the hair salon?

Before anyone says anything, I don’t mind spending a good amount of money on getting my hair done. I know hair stylists have bills to pay, and it’s a luxury, and I knew that going into it. I booked with someone for a cut & blowdry, and the deposit was half of the overall cost, but I also booked it on a day I would’ve received a student discount as they only offer that discount two days of the week. I was called that morning and told the hair stylist wasn’t in and I’d have to be rebooked, but because I work so much and really need a haircut, they could only get me in for two days later with someone else and that all the discount days were fully booked for the next few weeks. They automatically assigned me to another hairdresser, and I checked the booking later that day and saw that with who they’d reassigned me with I’d be charged over $30 more dollars than what I would’ve paid with the initial stylist if I booked with her. I called up the salon actually asking if I’d be charged and they told me I’d have to pay the extra to get my hair cut with her, and I argued that because I got no choice in who I was rebooked with and initially booked with someone who charged less. I’m not allowed to get my deposit back, and basically have to put up with the extra charge if I want to get my haircut, but am I being unreasonable about it? I’m not sure if I should argue it more when I go in because I wasn’t given any choice in the booking, or if this is completely reasonable