The abbreviation e.g. is short for the Latin phrase "exempli gratia," which in English means for example. If you enjoy tropical vacations (e.g. trips to the Caribbean or Mexico), you might want to consider Hawaii.
Use e.g. parenthetically, not in text. In straight text you should just say "for example." You are a good writer — for example, you've won a few awards. Even good writers need a good editor, so you should have a teacher or a friend check for common mistakes (e.g., typos, spelling errors, and subject-verb agreement errors) before you submit your work to a contest.