The truth on over-the-counter whitening products such as mouth rinses, toothpastes, and chewing gums, is that they don't actually whiten your teeth. What they do is help maintain and prolong the results from take-home or in-office whitening procedures.
One over-the-counter whitening product that does whiten teeth significantly are whitening strips, such as Crest 3D White (I recommend Gentle Routine), just be aware that they will only whiten your natural teeth, results vary, and if not used correctly they may cause mild to severe gum and/or tooth sensitivity. Using fluoride gel trays two weeks prior, during, and two weeks after whitening is always a good idea to help reduce tooth sensitivity.
Let me know if you have questions on teeth whitening, I love talking about how to keep pearly whites sparkling!