Do you have a DA polisher? They can work wonders if you know what your doing. They can virtually eliminate the chances of doing exactly what you did.
I would start by claying the entire panel, then use a medium cut polish and work your way up to a finishing polish. If you still have some light hazing you may have to go back over with medium cut polish again. Obviously you'll have to do the entire door panel and possibly (up to you) hit the other door panel and fender to blend it all together. Finally a sealant and a wax.
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2015 Altitude - Billet Silver
SRT Springs, Taillight Bezels, Red Start Button, Pedals & Grille Mesh, Black Lugs,
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Red LED 3157 Bulbs, 15% Tint, Polk DB Center Channel, Mopar All Weather Mats