I had a good chemistry class in high school. When I took chemistry in college in a good program for getting into medical school from, chemistry started at point zero. The fact I came in with a good background in chemistry did help, and makes it hard for me to judge if it could have been done with no starting knowledge of chemistry, but lacking chemistry knowledge shouldn’t hurt you too much. Don’t get me wrong, it’s not optimal. But it’s unlikely to be a situation where your prof will skip topics 1-10 because you’ve seen them in high school.
My suggestion would be to pick up a basic book (not a textbook, just a book) about chemistry and read it cover-to-cover. I’m a fan of Idiot’s Guides. I’ll tell you right now that IGs do make mistakes here and there that a seasoned chemist will pick out, but don’t worry about it. Your goal is to just gain a wide exposure. That way when you hear “chemical species” and “molecule” and “ion” on day one your head won’t be spinning. Also, don’t be afraid to send an e-mail to the prof before the first class to introduce yourself and ask if you should be concerned about your lack of background. This will be helpful later if you need help.
Calculus is a different kind of math. You need a strong grasp of algebra and trigonometry (trig is what we now tend to label “pre-calculus”). The big thing is that you can’t be a person who sees an equation, plugs shit in, and gets an answer. You need a deep enough understanding of algebra that you can look at an equation, understand what ever part of it means, and manipulate it in unique ways. I think that there’s an Aha! moment in calculus that once you start getting it, you’re good. It’s just reaching that point that’s the challenge, and reaching it early. And get extremely comfortable with f(x) notation.