I didn't take calculus in high school either. I did take college algebra in high school as a dual enrollment student. There are some concepts from college algebra that transfer over to college calculus like long division, logarithmic functions, and asymptotes. So yeah, you should take algebra before calculus. In my calculus class, they did go over the concepts I listed, but taking the algebra class beforehand did help me understand better.
Just make sure to go to office hours and tutoring if you are still struggling. I had to do that and I got an A, so it paid off.