No, lower profile tires will not help. Because if you have a more high performance lower profile tire on a larger wheel, you'll actually get "road tracking" as some call it, where your tires will follow irregularities in the road. My 18" tires follow road grooves that my 15" tires just roll right over.

I'd say if it's a constant and predictable problem, like it's pulling to one side constantly, an alignment should fix it. See if the dealer will re-align it under warranty.

If it's going back and forth both sides, there could be something more involved.