Do this with the windows open for ventilation: Put some ammonia in a spray bottle, spray the tint liberally then apply a piece of black plastic or a trash bag cut to size, on top of the wet ammonia. Let it sit a while (at least 30 minutes) SLOWLY pull the tint and trash bag off the glass. After...
It is most likely from the iron particles from brake dust, or rail dust from transporting on railroads. You can use a claybar to remove them and then wax the area with a decent polish such as Meguiars or 3M, it will help keep the particles from sticking to the paint.
Just get a random orbital polisher/buffer for around $50 and $20 for a decent polish and $20 for a decent wax (I suggest 3M or Meguiars)
It sounds like your swirls aren't very deep so you should be able to get by with this and is nearly impossible to mess up your finish if you don't know what...
a 13" blade might work as they are only 1/2" longer in each direction, if not you might have to downsize to an 11" blade. Trico and Anco both make 11" winter blades.