@mikemac actually gave you pretty solid advice. The main point being, don’t worry what your friends are taking. It has absolutely no bearing on you. You sound like a good student getting a solid base in precalc. Professors enjoy having students like you. In fact, they may prefer students like you - those with just a solid precalc background - over students having a weak calculus background.
You don’t have to retake pre-calculus, assuming you do well in your high school class and you learn how to think logically and reduce problems down to their basic forms. Too often students just memorize formulas to get through calculus, especially in high school. I think what mikemac was trying to convey to you is this will take lots of work but it’s totally within your capabilities. Make full use of all available resources - TA, study guides, study groups if that works for you, professor, tutors.