So I have a problem with my brakes that I'm not entirely sure how to resolve.

The rear brakes seem to be set too high for my wheels. When I squeeze the brakes, they actual pads end up touching the wheel itself, in addition to the rim.

The pad shoes are set as low as they can be on the brakes. I thought it might be simply that my pads were worn down, but after replacing the pads, I still have the same issue. No matter how I adjust them, one side is always touching the actual wheel when I brake.

Any ideas what I could do to resolve that? My lbs suggested dremeling out the dropout in the brake, so I could move the shoe a little further down... while I believe that would work, I also dont think I should HAVE to do that.... seems like there should be an easier fix.