I doubt that balance would be a problem unless you are having these issues at very high speeds or the wheel is very, very out of balance.
An out of round or bent wheel is a different issue. Set your bike on a stand so that the wheels can rotate freely. Give them a spin and watch closely. Fasten a marker of some sort from the frame to the edge of the wheel rim so that any up/down or left/right motion will be obvious.
If there is a large amount of side to side or up/down motion you may need a new rim. If there is a smaller amount it can be corrected by adjusting the spokes.
I have never been sucessful at adjusting spokes, but it can be done! I recommend taking the wheel to someone who has the gift....
Rod