You don't need any probability: the probability used in QM is so basic that you pick it up just from common sense.
You need linear algebra, but sometimes it is reviewed in the book itself or an appendix.
QM seems to use functional analysis, i.e., infinite dimensional linear algebra, but the truth is that you will do just fine if you understand the basic finite dimensional linear algebra in the usual linear algebra course and then pretend it is all true for Hilbert Spaces, too.
It would be nice if you had taken a course in ODE but the truth is, most ODE courses these days don't do the only topic you need in QM, which is the Frobenius theory for eq.s with a regular
singular point, so most QM teachers re-do the special case of that theory needed for the hydrogen atom anyway, sadly but wisely assuming that their students never learned it. An ordinary Calculus II course covers ODE basics like separation of variables and stuff. Review it.
I suggest using Dirac's book on QM! It uses very little maths, and a lot of physical insight.
The earlier edition of David Park is more standard and easy enough and can be understood
with one linear algebra course and Calc I, CalcII, and CalcIII.