Jesus never said don't go by the old testament.
He said Do not think that I came to destroy the Law or the Prophets.
Jesus further clarifies: “Whoever therefore breaks one of the least of these commandments, and teaches men so, shall be called least in the kingdom of heaven; but whoever does and teaches them, he shall be called great in the kingdom of heaven”
This people honors Me with their lips, but their heart is far from Me. And in vain they worship Me, teaching as doctrines the commandments of men.’ For laying aside the commandment of God, you hold the tradition of men … All too well you reject the commandment of God, that you may keep your tradition”