If you're sure you didn't have it before the flat, make sure the axel is firmly seated in the dropouts. It often happens that in our haste we think it is right, but it might not be.
A little wobble is not dangerous, but as you've noticed it is tough on brakes and your rims. If you grab the spokes in the wobble area, you'll notice that some will feel looser than the ones around them. This indicates a weakened wheel and should be trued.