Correct.

And Simon Peter answered and said, "Thou art the Christ, the Son of the living God." ¹⁷And Jesus answered and said to him, "Blessed are you, Simon Barjona, because flesh and blood did not reveal this to you, but My Father who is in heaven."  Matthew 16:16-17

Jesus says in John 4:24 that "God is spirit..."  It wasn't a person or thing having "flesh and blood" who had revealed this to Simon Peter.  Instead it was Jesus' Father in heaven who revealed this to Peter.

"Tell no one that I am the Christ":

Although Jesus truly was the Christ, the Son of the living God, Jesus asked his disciples to tell no one...until he was raised from the dead.

Matthew 16:20 says: "Then He warned the disciples that they should tell no one that He was the Christ." (NAS)

Mark 8:29-30 records the same event this way:

"And He continued by questioning them, "But who do you say that I am?" Peter answered and said to Him, "Thou art the Christ." And He warned them to tell no one about Him." Mark 8:29-30 (NAS)

In Luke 9:20-21, it says:

"And He said to them, "But who do you say that I am?" And Peter answered and said, "The Christ of God." But He warned them, and instructed them not to tell this to anyone," Luke 9:20-21 (NAS)

The first recorded time (after Jesus warned His disciples) that the disciples referred to Jesus as the Christ was after Jesus had been crucified...during the time when the church was established on the day of Pentecost in Acts 2 (see Acts 2:31-38).

"Therefore let all the house of Israel know for certain that God has made Him both Lord and Christ —this Jesus whom you crucified." Acts 2:26

After this point Jesus' disciples commonly referred to Him as the Christ.

Click on "Question 3" to continue...