Would the journalism department allow a sophomore in the internship class?

I am admittedly confused as to why you applied for an internship without working with your advisers. This all should have been sorted out before you ever applied. You particularly shouldn't have done this if you knew your college's policy in advance, which it appears you did. And you're not being prospected by the station -- you intentionally sought them out and applied for the job. I fear that it's going to make you look disorganized and foolish to the station, and that if you have to reapply next year, they're not going to take you as a result. This is not a good foot to start off on, and it's going to require some careful steps on your part to overcome it.

You might be able to do the internship, but you're going to need to request special permission from the college, and you're going to need to have a very good reason to give them for why you applied without consulting with them first. That's something you'll have to sort out with them directly, and if they tell you no, I would urge you to handle that as maturely as possible. Don't get on the college's bad side, especially since you'll need to do an internship in the future.

Doing the internship for no credit is likely not an option. Most television stations won't take on unpaid interns because their parent companies require them to compensate interns somehow for their work, and that usually means pay or credit. Since college credit is the cheaper option for them, obviously, they prefer students who can earn credit instead. If you do a credit-free internship, they may have to pay you, or pay you more than they would have otherwise, and it just creates a headache for them. In addition, companies of all sorts usually want students to earn credit for internships in order to keep them more responsible for doing their work.

I wish you the best, and while I don't mean to harp on you, I do hope you learn from the experience. Good luck with making this internship work -- I hope it all ends up working for you and that you have a good experience.

Do you have any credits from AP classes or dual enrollment from high school? If so, you might already have junior status. If not, you can still be an intern at the news station, you just won't receive credit for it. You can start interning now and once you're a junior, you can receive credit. Just because you don't get it noted on your transcript doesn't mean that you're not gaining experience.