No, I believe that He chose me, but I also believe that I could have turned away like the Rich Young Ruler.
According to your narrative, there is a pivot point. That being either turning away from Jesus as the Rich Young Ruler at the time of the episode recorded in Matthew 19:16-24 or following Jesus. These are two mutually exclusive choices:
(1) turn away
(2) follow
You answered the inquiry with "No, I believe that He chose me". Based on this answer, you wrote "No" that you do not believe that you chose Jesus as well as you testifying that Jesus chose you.
Back to the pivot point, which by definition is a point of choice per your narrative, since you wrote "No, I believe that He chose me", that would mean that a power outside of you made the choice to follow Jesus.
Now, let us sit at the feet of the Master:
"You did not choose Me but I chose you"
(John 15:16)
"apart from Me you can do nothing"
(John 15:5)
"I know My own"
(John 10:14)
The testimony of the Apostle Peter, whom you quoted earlier:
"Lord, You know all things"
(John 21:17)
The Apostle John recorded:
"Jesus answered them, 'Did I Myself not choose you, the twelve, and [yet] one of you is a devil?' Now He meant Judas [the son] of Simon Iscariot, for he, one of the twelve, was going to betray Him."
(John 6:70-71)
It is no small thing that the Lord Jesus knew that Judas Iscariot would betray Jesus because that is knowledge in advance. Jesus knows all things.
The Lord Jesus knows His Own. He set no limitations as to time nor place.
What can a believer do apart from Jesus? Nothing.
Not only are people incapable of choosing the Lord Jesus, it is He Who chooses.
This is powerful love. This is compassion. That God would take dead creatures and breath in Life. Concerning Life, the Lord Jesus said:
"Jesus said to him, 'I am the way, and the truth, and the life; no one comes to the Father but through Me.'"
(John 14:6)
Nicodemus seemed quite in a quandry (verse 4) with an exchange between him and the Lord Jesus Christ, yet Lord Jesus makes it clear in the Spirit of the Living God:
3 Jesus answered and said to him, "Truly, truly, I say to you, unless one is born again he cannot see the kingdom of God."
4 Nicodemus said to Him, "How can a man be born when he is old? He cannot enter a second time into his mother's womb and be born, can he?"
5 Jesus answered, "Truly, truly, I say to you, unless one is born of water and the Spirit he cannot enter into the kingdom of God.
6 "That which is born of the flesh is flesh, and that which is born of the Spirit is spirit.
7 "Do not be amazed that I said to you, 'You must be born again.'
8 "The wind blows where it wishes and you hear the sound of it, but do not know where it comes from and where it is going; so is everyone who is born of the Spirit."
Nicodemus appears to be trying to figure out how Nicodemus can work to achieve being born again, yet even in that moment Nicodemus defers to the Master. The Master explains that flesh begets flesh and the Spirit of God brings birth from God Almighty. Notice that in verse 8 that Lord Jesus says "you hear the sound of it, but do not know where it comes from and where it is going". That "you" is not the Spirit of God for the Spirit of God acts in accord with God (John 16:13), the God Who knows His own as well as knows all things. This is a wonderful act of redemption by God that defies fleshly understanding which explains Nicodemus' initial response in verse 4. God tells us that salvation is by God's grace for God's glory!