Should those who have faith in Christ seek their salvation through their own works, or anywhere else?
No, they should not, as everything necessary to salvation is found in Christ. To seek salvation through good works is a denial that Christ is the only Redeemer and Savior. Galatians 2:16: Know that a person is not justified by the works of the law, but by faith in Jesus Christ. So we, too, have put our faith in Christ Jesus that we may be justified by faith in Christ and not by the works of the law, because by the works of the law no one will be justified.