They feel that business is the only real major? As in, its the only major that you can enter a career with straight after undergrad? I'm confused. Do you want business, or medicine?
Biochem is not the funnest major to be "forced" into. I'm one of 5 B&MB majors at my school, and it isn't for everyone. Granted, you'll take these courses in med school (if thats what you want to do), but its not the best way to spend 4 years if you dont enjoy it. You have to really, really like it.
It doesn't sound like you're too crazy about med school. Do you really, I mean really, want to go into medicine, or do your parents have an influence on this decision? Its one thing to do what your parents want for high school, or even college (though thats a stretch), but this is the rest of your life. And if they're going to cut off the financial umbilical cord, so be it. It'll happen eventually, anyway.
Like i said before, do what you want, your parents have already been through school, its your turn. I'm sure that plenty of state college students get into medical school also. It about you, not your school. And who knows, in two or three years, you might decide that you want to become a lawyer, teacher, poet, CEO, or whatever. What happens if you discover that you absolutely hate biochemistry, and would rather die than regurgitate another organic formula? What good will the Biochem degree do then?
So yeah, to answer your original question, in my opinion, college calculus is easier than high school calculus.. or even precalculus. If you're that worried about it, retake precalculus before you take calc. Also, get to know your professor on a one-to-one basis (no bribing), so that when you're having trouble, you can ask him/her about it then and there. That'd also pave the way for a future LOR. Same goes for all professors. Even if you're breezing through organic chem (which won't happen), ask for help. Clarify. Ask questions. In college, there are (almost) no dumb questions. And teachers will respect you more for having the guts.