I am a junior in a South Carolina high school and my class is having a New York trip! I was wanting to know if I can fly there. I have been approved for daca and I have my drivers license. Am I able to go on this trip and am I able to fly in the US?

As long as your parents allow it I don't see why not.

I'm not sure why this is under immigration law. Traveling within the states has nothing to do with immigration.

DACA does have to do with immigration. I too have never heard of immigration affecting movement among the US states.
I know nothing about it, but here's the site:
Consideration of Deferred Action for Childhood Arrivals (DACA) | USCIS (http://www.uscis.gov/humanitarian/consideration-deferred-action-childhood-arrivals-daca)

As a minor child (under 18), all questions need to be asked of parents first and school administration second.

The link Joypulv posted mentions some circumstances under which persons who have been approved for DACA may not travel. That, however, refers to international travel. Traveling from South Carolina to New York and back would be completely within the US, and thus not a problem.

With parent approval, there are even programs for younger children to fly.

Generally when travelling inside the U.S. nobody will ask you about your immigration status. TSA does not have the jurisdiction to ask about, nor are trained to deal with, immigration status; they just care about ID (and ID is not required for people under 18). Local and state police (except perhaps for places like Arizona and Georgia) don't generally care about immigration status because it's a federal matter.

Being under DACA makes you not deportable. Make sure to bring your DACA approval, in the extremely unlikely chance you do get checked by Border Patrol or something.