is "You Worry Not" a correct phrase?

In older forms of the language, this construction has been used repeatedly by great poets like Shakespeare, so it can't be considered "wrong", just dated and out of use. Personally, I would think it is poetic rather than wrong.

Another way to make this phrase more of a promise is Don't you worry, which is more widely used today.

The equivalent of "love me not" would be "worry you not". Similarly, it sounds antiquated, and one might initially feel it looks wrong.

That said, it is just as much of a command (as is "love me not")!

As @Irene and @RandomIdeaEnglish pointed out on another answer, other forms would better convey your meaning.