Sounds like you're making exactly the right decision!. Maybe you could bring your appointment forward from Wednesday- ask for an emergency appointment.
Though hang on in there, if you've got strategies you've used before to stop cutting could you lean on these. Although drinking can be a way of blotting out things and making things seem a little better it does leave you vulnerable and maybe more likely to self harm (sorry you probably know this) but if you can replace it with something? Go out? Go for a walk?.
But get all the help you can, as you know cutting can be an addiction and hard to stop. Best wishes.