can you describe the process you used to wash the car? did you also wax? there's a certain amount of time you're supposed to hold off on waxing a new paint job. i forget what that is.
it's easier than you might think to swirl your paint. especially on a soft paint, which brings me to the next question, where did you get your paint job done?
i'm also going to assume that it's a darker color.
if the swirling is light, you should be able to remove it with a good polish by hand. if that's not working for you; you may want to start looking into a machine. a good random orbital polisher can be had for pretty cheap nowadays (a bit over $100), and then you'll need to buy the pads, etc.
anyway, get back to me with answers to my questions, and we'll try to help you further.