RE: New Starter
welcome to the board, i expect the reason you are swaying is because your stabiliser muscles are not up to the same weight as your core muscles. This will improve, just make sure you have someone on hand incase you get stuck.
Like the guys say, form is most important, especially at the beginning of your training. As you adjust to the training you should find the swaying stops. Just keep at it and don't try to run before you can walk.