Is it egotistical to think that a God would die for you?
This is a deeply theological question. Let me give you a two part answer.
First, it is egotistical from a theological point of view to believe that God would die for you, if you make the assumption that you were somehow so precious that God had to die for you. In other words, Christian theology (classically speaking) affirms the death of Christ for sinner, but does not presuppose the worth of sinners. What is, therefore, underlined in the grace of God. This is why Paul says in Ephesians 2:1:
"We were dead in our sins and and transgressions." Two verses later he even writes: "We were by nature objects of the wrath of God."
Second, if a person believes in the death of God for his people based on the mercy, grace and love of God, then it is not egotistical. Why? Again as Ephesians 1:3-14 states three times. God did it all for the praise of his glorious grace. This includes the death of Christ. This act was an act of demonstrating his glorious grace.
From these two points, it is really a matter of perspective. C.S. Lewis is one of the great Christian authors who will give you an insightful look at Christian theology.