Is it possible to double major outside of your college? Like if I was majoring in communications in Annenberg, would I be able to major in like English or computer science or something too?
yes indeed.
USC actually encourages students to major and / or minor in diverse areas.
for some majors, like CS, you may have to apply to the college that offers that major- i.e. Vertibi for CS. But normally one can do any 2 majors- but getting the class schedules for the required classes in each major to work is what can trip up plans for double majoring.
@menloparkmom thank you!!! 
My son who is a CS major in Viterbi was barely able to squeeze in a minor and that is with a lot of AP credits helping out. And the sequencing of the courses as well as whether they are even offered in the semester you want to take them just adds to the complexity.
So yes you could double major but it is unlikely unless you do summer school and/or possibly finish in 5 years.
English and communications as a double is much more likely than adding an engineering (CS) degree as a second/dbl major - there is no course overlap at all. My CS major will finish with his major plus two minors and is only staying the last semester of senior year to do classes for the second minor. (So would have graduated in 3 1/2 for major & minor.) The minors are in science/math. Different schools than Viterbi, but still complimentary.
But the good thing is if you are willing to put in the time and energy you can do about anything you want at USC in terms of double majors/minors, at least you have the choice and opportunity to do so. Not true at all schools.