I have to admit I don't know anything about medical schools in Canada. I can only tell you about how things work in the US.

I don't know what you consider as the math course for 12th year students (referred to as a high school senior in the US). In the US, the typical 12th year math course would be pre-calc, although many students who would be considering medical school in college will take calculus their last year of high school as an advanced placement (AP) course - meaning they can get college credit for taking the class in high school.

For psychology (in the US), you wouldn't need to know calculus. You would likely take a statistics class at some time during your training, but I don't know that they'd require any specific level of math prior to that. You would basically need whatever level math is required to get into college.

For medical school, in the US, calculus is not required but I think most pre-med students have taken calculus. You need to go to medical school to be a psychiatrist.

Sorry I can't be more helpful, but I'm just not that familiar with the Canadian system.