This isn't mess for the sake of it. Your regulars like to message you. New people use whatever they find first. The problem is that the diary is being updated last, by hand, from five directions.
Give people one good way to book, and keep the door open
Put one booking link where people will actually see it: in your Instagram profile, in a saved reply, on your website if you have one, and on the card on the till. The link should show your real availability, not a form that just emails you another message to deal with later.
Write a short saved reply for the accounts you already use: thanks, here's how to book, and if they need something unusual they can say so. You can still take a booking by message when you want to. The aim is that most of them don't need you to be the go-between.
Turn on a reminder for the day before, with an easy way for someone to move the appointment rather than just not turning up. Write that reminder yourself, in your voice, so it doesn't sound like a machine. If your booking tool already does this, use it. If you haven't looked at the settings in a year, look now.
Everything should feed one diary. If the phone book, the paper book and the app can disagree, they will. Choose one as the official diary and make the others point at it, even if that takes a week of being strict with yourself.
Some regulars will always prefer to message you, and that's fine. Keep a little space in the diary for those, or book them in yourself from the message, rather than running a second informal list in your head.
Shaped to your salon, not an off-the-shelf package
We'd set up one booking page showing your real availability, shaped to your salon, not an off-the-shelf package. Often that is a tool you already have. Friendly automatic replies on your messages would point people to that page, and anything that needs a person would still come to you. You'd approve the wording before those replies go out.
Reminders would go out the day before, with an easy way to move the appointment rather than just not turning up. You'd approve that wording too. Everything would feed one diary, so the phone, the messages and the booking page can't double book you.
The booking tool would be yours, in your name, paid for on your card. We charge for setting it up around how you already work, and for looking after it if you want us to. If we step back, the page, the diary and the reminders stay where they are.
Clients could then book themselves at 11pm without waiting for you to reply. You'd have fewer double bookings and fewer empty chairs. Your evenings would come back, at least in part, because "have you got anything on Saturday?" would no longer be a conversation you have to have by hand, every time.