Actually, Jesus said very clearly that He was the I AM, or God. It does not come through in the English, possibly because the translators thought it was bad grammar? I don't know. But Jesus stated several times "Ego eimi" I am I AM. One time is in John 8:24. The Greek states that Jesus says if they do not believe EGO EIMI, or I am I AM, they will die in their sins. There are a number of other places. The Pharisees understood distinctly what Jesus was claiming, for you see them ready to stone Him in John 10:31, "but Jesus said to them, "I have shown you many great miracles from the Father. For which of these do you stone me?"
"We are not stoning you for any of them," replied the Jews, "but for blasphemy, because you, a mere man, claim to be God."
Having called Himself God, yes, Jesus then stated that the Holy Spirit was also God. Look at John 14:16:
"And I will ask the Father, and he will give you another Counselor to be with you forever -- the Spirit of Truth."
First of all, a few verses earlier (v. 6), Jesus had said HE is The Truth. The Holy Spirit, being the Spirit of Truth is then at the very least part of Jesus! However, there is more, and again this does not show up in the English. It is the word translated 'another'. There are two Greek words for 'another:' allos and heteros. Heteros would be used in a sentence such as "While you were busy talking to your sister, I was talking to another person." The 'another' is totally different. Allos is quite different -- it means one exactly the same as the first. "I broke your vase! I'm so sorry! I'll get you another one." If, in Greek, 'allos' is used there, the meaning is that one will be bought that is exactly the same as the one broken.
When Jesus said He would ask the Father and the Father would send another counsellor, the word 'allos' was used. The Holy Spirit is exactly the same as Jesus in nature: He is God.
So yes, Jesus claimed explicitly to be God, and when He said the Holy Spirit was 'another' Him, the word used meant exactly alike.
Did Jesus say 'worship Me'? No, but when Thomas addressed Him as 'my Lord and my God,' Jesus accepted the worship and did not correct Him. When Peter identified Jesus as the Messiah, the Son of God, Jesus agreed, telling Peter that God had revealed that to him.
Nor did Jesus ever address Mary as 'mother' as recorded in the Bible! The only times He addressed her, He called her 'woman.' This is also how He addressed Mary Magdalene outside the tomb on Resurrection Morning. Not quite what the Catholics would like, but then I don't think the Lord likes Catholicism much, either.