By "fulfilling the law" basically Jesus was claiming that he was the messiah that was referenced heavily in the law (which refers to the old testament).
You are right, but Jesus fulfilled Scripture in other ways too. I'm going to take a "rabbi trail" here... In Judaism, to "fulfill" something means to interpret it correctly. This is what Jesus did through the way He lived His life. He full-filled it not only by keeping the commands of the law, but by filling it full of its true meaning.
Moreover, that He fulfilled the law does not mean that we, His followers , are to ignore the law's commandments, which are "holy, just, and good" (Romans 7:12).
For sin shall not be your master, because you are not under law, but under grace. Romans 6:14
Shows that Christians are not bound by the Old Testament laws because Jesus fulfilled them.
Look at what Paul is saying. It's not that keeping the law makes sin your master; rather, legalistic observance of G-d's commands without having understood and received His grace is what makes sin your master.
It should be noted that the ancient Greek language did not have a word for "legalism." There was only this word (in Rom. 6:14, nomon), which is always simplistically rendered as "law" in English.
Look at the context, using another version (CJB):
14 For sin will not have authority over you; because you are not under legalism but under grace. 15 Therefore, what conclusion should we reach? "Let's go on sinning, because we're not under legalism but under grace"? Heaven forbid! 16 Don't you know that if you present yourselves to someone as obedient slaves, then, of the one whom you are obeying, you are slaves - whether of sin, which leads to death, or of obedience, which leads to being made righteous? 17 By G-d's grace, you, who were once slaves to sin, obeyed from your heart the pattern of teaching to which you were exposed; 18 and after you had been set free from sin, you became enslaved to righteousness. 19 (I am using popular language because your human nature is so weak.) For just as you used to offer your various parts as slaves to impurity and lawlessness, which led to more lawlessness; so now offer your various parts as slaves to righteousness, which leads to being made holy, set apart for G-d.
Is Paul saying that lawlessness is bad, but keeping the law is also bad? Sounds like a lose/lose situation for humanity. But no; Paul professes, "we confirm/uphold/establish (KJV) the law" (Rom. 3:31) But only a keeping of the law that is grounded in a relationship of trusting faithfulness in G-d and His grace for us. Christians nearly always miss this distinction.
There are several references to where Jesus goes opposes society's norm such as Mark 2:23-28 where Jesus plucked grain on the Sabbath.
He did what was "unlawful" regarding the Sabbath only according to the Pharisaic rabbinical laws. He did not violate G-d's law concerning the Sabbath. He simply held to a less burdensome practice of keeping of Shabbat.
And another instance where he saved a woman from stoning because of adultery*
Here, Jesus was, in fact, going strictly by the Book (Deuteronomy 17):
2 "If there is found among you, within any of your gates [in any city] that the L-RD your G-d gives you, a man or woman who does what the L-RD your G-d sees as wicked, ... 4 and it is told to you, or you hear about it; then you are to investigate the matter diligently. If it is true, if it is confirmed that such detestable things are being done in Isra'el; 5 then you are to bring the man or woman who has done this wicked thing to your city gates, and stone that man or woman to death. 6 The death sentence is to be carried out only if there was testimony from two or three witnesses; he may not be sentenced to death on the testimony of only one witness. 7 The witnesses are to be the first to stone him to death; afterwards, all the people are to stone him. Thus you will put an end to this wickedness among you.
Jesus said to the woman's accusers, "The one of you who is without sin, let him be the first to throw a stone at her." (John 8:7) By asking this, the Rabbi/Torah-Lawyer Jesus was attempting to summon a witness. We don't know what He wrote in the sand before asking the question, but it seems that He managed to shame them so that they wouldn't respond. Thus the Defense won the case by default because the Plaintiff could not produce confident witnesses to cast the first stone. Jesus showed grace to the adulteress, but He did not abrogate the Law.
10 Standing up, Yeshua said to her, "Where are they? Has no one condemned you?" 11 She said, "No one, Sir." Yeshua said, "Neither do I condemn you. Now go, and don't sin any more."
The story ends with Jesus the Messiah again confirming and advocating observance of His Father's Torah/law.
The take-away message? Grace AND law. Like the sinful woman, we too have sinned. So our gratitude for G-d's grace to us should inspire us to keep His law and sin no more.