This is nothing to do with British or American usage.
Only wrong is possible here.
However, you could make an argument that adding a comma before wrongly is possible. This would be using wrongly as a comment adverb modifying the clause She did it.
She did it, wrongly. = It was wrong of her to do it.
But, without the comma (or in speech a pause) the final adverb would be a manner adverb modifying the verb did.
She did it wrong. = She did it in an incorrect way.