Law firms generally don't have a reason to have undergrad interns. I'd recommend interning places that employ lawyers or just that will give you legal/writing experience while in undergrad (tons of those in DC!)

I also recommend working as a paralegal or in some other role where you are directly working for lawyers before law school. It will give you a much better sense of what lawyers do and if it's the job for you. Highly recommend working before law school!

But in short, don't stress about finding an internship at a law firm--that's not usual or expected.

Source: am a lawyer, have worked at three DC law firms