Tracy, is what you have paint drips and runs from repainting or is it a dusty chalky white look that looks like the paint has come off in a powder from the rain and run onto the brick. If you are talking about paint drips and runs, I agree with Steve. If you have chalking, you might go to a yard that specializes in brick and concrete. They will have chemicals that can be used very successfully. You need to talk to someone that really knows how to do this and how to safely handle the products.