If it is your intention to enter engineering and attend a prestigious university such as UC San Diego (my Alma Mater) or UCLA (or Berkeley, Stanford, USC, etc.), it would be very tough for you to gain admittance without having taken 2-3 science courses during high school, particularly physics (Note the correct spelling). Calculus would also be good to have under your belt while in high school, although not mandatory. I am surprised your high school counselor did not tell you this earlier in your high school career. If it is at all possible DO take a physics course.
Good Luck, Pete Sturtevant, P.E.