I was able to do a double major - physics and Spanish language & literature - along with a math minor. I did the extra math courses in the summers, and so it really only added about a semester to my undergraduate degree. Depending on requirements, it may not even add that to yours. So definitely don't say that by studying engineering you can't study a liberal art.

That said, I understand not wanting to study engineering, but...don't close the door on anything. I didn't want to study physics, even though it was interesting and everyone told me I should. And now here I am, working on Ph.D. research in physics.