Two things come to mind that could have happened. First, the scratch remover you used left its own micro-marring, leaving the finish hazed and cloudy. To solve this, you will need to apply a milder product that will remove the micro-marring, while not instilling any additional marring itself. Good options available OTC would be Meguiar's Swirl-X or Ultimate Polish (NOT Ultimate Compound!).

The second possibility is that you polished straight through the clear coat, and into the base/color coat. If this is the case, then the only way to fix this would, unfortunately, be a repaint of the affected panel. Hopefully, this is not the case - a picture would definitely be of help in attempting to determine which it is. Another way to tell is to try some of the scratch remover and rub it on the affected area - is the applicator you're using picking up color? If it is, then you likely have polished through the clear.

As to your question whether wax will fix this? An aggressive all-in-one product, which has abrasives, would have the same effect as a polish, but most waxes available OTC, including most cleaner waxes, would not really do anything to permanently fix the situation. Some waxes or glazes might have fillers that could temporarily mask the issue, but when the product wears off, the hazing will re-appear.

Oh, one final point - while it can be tempting to try and hit every little scratch that you incur on the car, it is generally not a good idea to do so. Remember that to "remove" scratches, you are leveling the paint to the level of the scratch - this means that you are abrading clear coat whenever you use these "scratch remover" products; and you only have a thin, finite layer of clear on the car. If I may be so bold, I would suggest reading up on proper washing techniques to minimize swirls and scratches on the paint, and perform a general polishing session only annually, if not a longer interval; as always, it is better to prevent the damage than have to repair it.