If I'm taking Algebra 1 right now in freshman year, but I only can take 1 course of math each year, is it okay if I only get up to Pre-Calculus at senior year?

Hi, in general, I'm sure this would be fine.  However, if you have your eye on a University that has a top 10-20 ranking for Engineering, it may not be enough.  Not being an expert in college admissions, the safest answer is to contact the particular University for advice.  I have heard that Universities are seeking to diversify their ranks but I am sure they also do not want to "play favorites" to female candidates either.  Each University has their own acceptance criterion.  The more prestigious it's reputation, the more difficult it will be to get in.  I cannot imagine that a typical State University would look away from students that don't make it to Calculus in high school.  If you are planning to go to a typical school that is not highly ranked, I am sure pre-calc is fine.