A double negative such as "didn't do nothing" is, in my opinion, not a very recommendable way of a speech. It usually sounds a bit unsophisticated except when you intend its use for a certain purpose. You suggested very wisely that it be replaced with an "anything" in the given context.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.
One of the similar examples of them could be, "You ain't seen nothing yet."