You have the right by the Washington Administrative Code to inspect your employee file at least annually. Ask to review it and see if there is a written record of the incident and action your describe.
If there is, you have the right to place a statement in your file with your version. There is no way to force the employer to resolve this issue, that is far as it goes.
You have not suffered adverse employment action just by being relocated. You don't state whether the relocation is to another state, another city, another outlet in the same city, or whether it is within the current building. If someone maliciously made up the allegations, you could sue them for defamation, but I don't know what damages you have suffered, if any, because relocation by itself does not tell me how you are being harmed.