Can faith and grace alone save us?

Most religious institutions and leaders teach that we are under the New covenant and that the old testament laws are done away with if we believe in Christ. They say that we are no longer under the law but that we are saved by grace and faith in the Messiah Yahshua Ha Mashiach/ Jesus Christ. We cannot be saved by our works or by keeping the law ( Torah). Of course only the blood of Jesus can save anyone as we have all sinned and are worthy of death. What does the word tell us about our works? Can our faith alone save us or will we be judged by our works? If we are born again in Christ does this not require repentance and a change in behavior? Let's see what the New Testament writings of the bible actually say.