Yes, Jesus said He was God. For instance, He said to the Jews: “I and the Father are one” (John 10:30), and “If God were your Father, you would love me, for I proceeded and came forth from God; I came not of my own accord, but he sent me… But you have not known him; I know him. If I said, I do not know him, I should be a liar like you; but I do know him and I keep his word… Truly, truly, I say to you, before Abraham was, I am” [i.e. Pure Existence having neither beginning nor ending, existing only in the eternal present] (John 8:42, 55, 58).
Men come to believe in God because He shows something of Himself to them. Catholics believe in what the Catholic Church teaches about Christ because they have the supernatural gift of faith. Thus, God the Son revealed Himself in what He said and did, how He lived with others, and by what He revealed of His thoughts and feelings. He revealed more of Himself than we can fully understand. Nevertheless, through faith and the virtue of love, we can understand a great deal about Him.
Jesus is the center of our Catholic faith. Everything that He said and did is important, because in Him we find God our Father and come to believe in Him. Jesus is our Way, our Truth, and our Life (cf. John 14:6).