Bike sways to the right

if it swerves to the right, it usually indicates that either A] frame is bent or B] forks are bent or C] both are bent.

it's better if it B] cos its easier to correct.

in any case, you will need to see a bike shop with "proper" mechanic that can identify the problem, and then fix it appropriately.

unless that is you want to try finding out yourself what is bent.... Sheldon has a rough and ready method for gauging the straightness of a frame... and you only need a long piece of string to do it. as for fixing it yourself, hmm, that's a bit difficult without a jig of some sort

whack the ends of your forks in a grid and give them a good kickin