I am in total agreement with you. Roman 3:24 says that we are justified freely by his grace through the redemption that is in Jesus Christ. Romans 2-4 points out that the law was a schoolmaster, showing what was right and wrong but it was incomplete, since in verse 3 it is to be noted that the law was weak, so that the righteousness of the law was fulfilled through Christ. The book of Romans gives a good exposition on the law and grace, Romans 5: 17-21 confirms all that you have written. If we look at 20, the law entered that the offence might abound, but where sin abound grace did much more abound and that sin reigned to death but grace unto life eternal. Blessings