Law and Love in Our Relationship to Others

If "love is the fulfilling of the law," does love replace the Old Testament law (the Ten Commandments or the Mosaic Law)?

And is there a contradiction between what the Apostle Paul said in Romans 8:3-4 about "the righteousness of the law being fulfilled in us" by the Jesus Christ condemning sin in the flesh and what he says in Romans 13:8-10 about love fulfilling the law? Can I become righteous simply by being loving?