Since soap is basic (pH) and nothing has happened, it sounds like the streaks may be etching (Acids and Bases mixed together neutralize each other). Acid rain causes the same etching in windows.
I used a Mr. Clean Magic Eraser soaked in distilled white vinegar. Made my windows crystal clear with no more streaking when it rains. It reflects so well, it's crazy. I would be willing to bet that the eraser should be able to help. For $3, it's worth a shot. The vinegar is safe for your car, but afterwards, I would rinse your car to remove the leftover vinegar. I don't think it'll cause problems, but better to be safe than sorry, right?
A good
glass polish should work as well, but will be more expensive. Glass Scrub comes to mind, although I don't know the company who makes it. If you go to CarQuest, DuraGloss (or similar, I can't remember) has a good glass polish as well.