Land an internship without any work experience.?

I'm a computer science major in my second year at college. I've never worked in my life, like not even a cashier or anything. My parents pay for my college tuition and give me an allowance which is enough for my needs consisting of mostly food, gas, and investing. I don't see the point in such part-time jobs and would like to know if it is possible to get an internship without any work experience. I am pretty experienced in my major, more than most people at my age, as I have been self-teaching my self a lot of stuff ever since 7th grade.

My parents say that I should work a small part time job before an internship. Is that necessary? How hard would it be to land an internship considering I have knowledge in computer science but without any work experience? What would I include on my resume?