If you haven't figured out what the problem is yet, here are a few suggestions:

1. Make sure brake lever (on handlebar) is not fully engaged (like when one is braking
hard).

As for the brake caliper rubbing/pushed up against the rear rim:

1. Make sure the bolt anchoring the affected side to the frame isn't torqued down
too tight.

2. Make sure that same bolt isn't too loose and the return spring (right terminology?)
has not disengaged with it's small hole on the frame.