An unseated axle in the dropouts could cause the wheel to be off center and rub on the side of the brake, but it won't make it wobble.
It's very likely the tire bead did not seat on the rim correctly making part of it bulge more, which would look kind of like a wobble. Let almost all air out of the tire then go around it squeezing and flexing it (twisting or rolling side to side) to try and get the bead seated evenly then re-inflate to normal pressure.
For the brake, make sure the springs on both sides are hooked up. Also that the axle is seated in the dropouts before tightening it.