Hey TheIllusion,
just to tack on to what's already been discussed -
expanding your vocabulary is great, but before you commit to doing so, please do keep in mind that using words with a lot of syllables won't necessarily improve the 'sophistication' of your essays. As you work on your vocabulary, also try to work on increasing the overall fluidity, pacing, and cohesiveness of your writing. If you only try to throw long, uncommon and/or esoteric words into your essays, it will stick out like Will Ferrel in Elf and make your writing feel awkward and forced, when what you want is natural and, well, unforced.
To improve, the best thing that you can do is to get your hands on as much quality written material as possible. Whether it be sample essays, works of fiction or famous speeches, just try to expose yourself to good writing and absorb as much of it as you can. Perhaps, to help you remember new or unfamiliar words, it might be handy to keep a notes folder in your phone/computer with all of the words that you learn in your readings, along with a self written definition. This will certainly help you expand your vocabulary more efficiently.
As an aside, don't feel like you need to have an amazing vocabulary in order to do well. Mine is also quite ordinary, but I made up for it by focusing on the quality of my ideas and being genuine in what I wrote. These two attributes are just as important, if not more.