As far as I know, you do not need to take chemistry to be a psychologist, but you would need it to become a psychiatrist. I don't think you will need chemistry to get accepted into a college, but you may want to check with your guidance counselor at your high school.

While in college, as a psychology major, you will probably need to take some science classes, but I would guess most colleges don't require chemistry to major in psychology. And I would guess there are few, if any, psychology courses that would require chemistry as a prerequisite. After college, you'd enter a graduate program in psychology to obtain further training in therapy and psychological evaluation, but chemistry would definitely not be part of the picture.

To clarify, psychologists almost universally do not prescribe medications, and you do not go to medical school to be a psychologist. Most psychiatrists these days do prescribe medications, and you do need to go to medical school to be a psychiatrist. You definitely need chemistry (included general chemistry, organic chemistry, and in medical school biochemistry) to be a psychiatrist.

As for career paths for psychologists, almost none include prescribing medications. Most are involved primarily in providing individual therapy to people, and many also provide group therapy and psychological testing.