Your phrase "my worrying about it" is correct. Many native speakers prefer to say "me worrying about it," but technically this is wrong. In casual speech, many native speakers would also use "by" the way you've done in this sentence, so although it's not quite right, it doesn't sound too bad. It would be more correct to replace "by" with something like "because of" or "due to." "Nothing will change because of my worrying about it." If you want to use "by," the sentence should be in passive voice: "Nothing will be changed by my worrying about it." To sound more natural, a better structure would be either "I can't change anything by worrying about it" or "[My] worrying about it won't change anything."

Nothing will change by me worrying about it.