First of all, you sound like a good student, someone who knows how to start and finish homework assignments and prepare for tests your teachers tell you about ahead of time. Now, how is quiz-taking different from your other classroom experiences?
Quizzes usually "pop" out of nowhere. Teachers like to find out where you stand in your studies as you learn over time. A quiz can tell you and your teachers how much information has "stuck" with you at any given moment, meaning that you're able to apply what you've learned.
A student may do well on a test if he or she memorizes a list of facts or knows enough about a subject to write a few paragraphs. Quizzes, however, call for you to show what you know without preparation. The surprise element may throw you off. After all, you're an organized person who likes to have fair warning when you're expected to perform.
Interestingly, quizzes can be a lot like life itself — full of surprises. The key is to expect the unexpected, which can help you as you meet other challenges along the way. To get better at quiz-taking, take a look at how your friends handle the "heat" when faced with a pop quiz. Do they freak out or jump right in? If you find someone who's cool with quizzes, ask her how she does it.
The good study habits you already have can help pull you out of panic mode when a quiz crosses your desk. Just relax, remind yourself that you know the material, and realize that you will get better — with practice, which is all the preparation you need.