Is it Biblical to think that Jesus died for me specifically? I know that He died for the whole world, but is it Biblical to think of Jesus as coming to die specifically for me? Is it possible that I could worship my own self made image of Christ rather then the real Jesus if I think of Him as dying specifically for me? Thanks.
In 1 Timothy 1:12-17, Paul - or someone writing as him - says (NRSV translation):
The author describes himself as being the pre-eminent sinner, although (from context) we know that he does not mean that he is actually worse than other people. Rather, his intention is to say that whenever anyone sins, he or she is condemned; and that everyone who is saved from the domination of sin is saved by Christ. The author counts himself as the chief of sinners because there is no greater sinner he can hide behind. There is no excuse for us. We can all describe ourselves in this way - but equally, we can all say "Jesus came to save me". And because of this knowledge, we must be careful to remember (as you point out) that the same is true for other people - Jesus did not come to save only me.
In response to your clarification:
You would like to know whether Jesus had you, specifically, in mind during his Passion. What we know from Scripture is that Jesus "gave his life as a ransom for many" (Matthew 20:28), and that "he died for all" to "reconcile us to himself", "not counting our trespasses against us" (2 Corinthians 5:15, 18-19). This act of reconciliation unites us with him in love; "our old self was crucified with him" (Romans 6:6) and now "we abide in him and he in us" (1 John 4:13). Further, it is written (Isaiah 53:4-6 and partially quoted in Matthew 8:17):
It is certain that every sin was part of his burden on the cross, including even those sins yet to happen. If this were not so, then our sins could not be redeemed, and we could not be united with him.
Jesus certainly suffered in his crucifixion, as the Gospels attest. We might argue about the extent to which he was conscious of each sin individually. While some would say that Jesus in his earthly life had only a human intellect, the transcendent nature of the Passion is surely a plausible candidate for an exception. In any case, he felt the pain of every sin, including yours and mine, regardless of precisely how he felt it.
"Christ died for all" God loved the people of this world so much that He gave His one and only Son Jesus Christ(John 3:16). The Bible doesn't say Jesus died only for the righteous or the Israelites, but He died for all mankind.
"Am I included?" The Bible says that Jesus died for sinners.
How does that include me? What can convince me that I am a sinner?
Even though you have not committed any crime outwardly, if you have evil thoughts in your heart, you are already a sinner. If you think that your heart is pure, you don't need Jesus to die for you. But if you are convinced that "all have sinned" (Romans 3:23), you indeed need the righteous Son of God to die for you. After accepting the fact that you are a sinner, then you can say with confident, "Jesus died for me".
"Jesus died only for me?" Saying that Jesus Christ died for me and me alone is egoistic, self centered and greedy. It means you want Heaven only for yourself and you don't want others to come. God desires everyone to be in Heaven with Him forever, and not only one person. You like it or not, there will be countless people in Heaven.
The answer is YES, YES, YES!
True saving faith involves personal engagement with the Savior, personally applying His work and all it has secured, Christ died in our place, substitutionarily. So the answer is yes
Jesus said while living as a human he knew who belongs to him. Revelation says the death of Christ was planned from the beginning of this world. If God could name all the stars in heaven, yes, He could name all of us and the divine nature of Jesus surely knew for who he was dying.
If you believe in the doctrine of Election, as I do, it is easy to understand that Jesus knew me in the eternity and died for me specifically, but not only me of course.
On the other hand, if your belief is that man has free will to accept salvation so Christ paid for all sins of all men in a generic way and is up to you to accept or not the salvation, it is more difficult to conciliate Jesus dying specifically for anyone. Nevertheless you can also believe that Jesus foreknew you would repent and believe in the Gospel so He knew He was dying for you.