There's really no chance to "screw anything up" with this application process.
I'm assuming you're on some site that lets you search for a whole bunch of different scholarships? If not, I recommend finding one. There are a bunch of them floating around the internet, though, and they'll all link you to plenty of scholarships.
Once you've found a bunch you can apply to, apply. Go crazy. A good chunk of them won't even ask you to write an essay, so just enter your information and move on to the next one. The ones that don't ask for much are harder to get anything from, though (as most of them are just choosing 1 winner out of a bunch of nearly identical applicants), but it still doesn't hurt to apply. As for the ones where you do have to write an essay, that's a bit more time-consuming (unless you can manage to re-use the same essay for multiple apps, but, that's not always a possibility), so take a look at how much money each one offers and how many winners each one will choose. Place higher priority on the ones where it's more realistic that you might win -- saves you some time.
But yeah, no reason to be hesitant. The worst that could happen is you just don't get picked for too many scholarships, but, there's nothing you can do that'll really hurt you in the application process, so, go crazy. The more you apply to, the better your odds of winning something.
Edit: And I should stress that there are plenty of scholarships not affiliated with your school that you should seek out (which was kind of what I was referring to in that last post). Obviously, the one affiliated with your school is the one you should probably place as highest priority, as you're most likely to get something from it, but uh, there are plenty of other scholarships where all you have to do is enter in a bunch of information a bunch of times and, well, like I said, no reason not to with those.
