"Do not worry about your life"
Some time ago, SFH asked, "How does worry play into our love of God? IE: worrying about things in our lives that happen, our crosses, is that not loving God with all our hearts minds, souls and strengths?" Thanks, SFH; let's first look at some things our Lord said about worry. "Do not worry about your life...Can any of you by worrying add a moment to your life-span? your Father knows (the things) that you need" (Lk 12:22,30).
Also, in last Sunday's Gospel, he warned against our hearts getting wrapped up in the anxiety of everyday living: "Beware that your hearts do not become drowsy from carousing and drunkenness and the anxieties of daily life, and that day catch you by surprise like a trap" (Lk 21:34).
Now, these passages might not speak exactly to what you're asking because Christ is referring more to mundane things about which we worry. You are asking about more serious matters, ones that involve human suffering. But, the fundamental point from God is that He does not want us to worry. One way to put it may be to say that worry is natural, but trust is supernatural.
Christ calls us to live lives of faith, hope, and love. In some situations, He calls us to have extraordinary, or even heroic, virtue in these areas. In the early Church, Christians had all kinds of things to worry about, all kinds of crosses; death was certainly one of them. Even if it death itself that is the fear or worry, they (and all martyrs) give us the example to continue to love God, believe that He is with them, and hope for eternal life. Did they live it perfectly? No. I would imagine that worry crept in from time to time. Worry is a sign of imperfect love for and faith in God. It's not until we reach the Kingdom that we will love God perfectly. But, we are on the path of perfection, especially in regards to faith, hope, and love.
Romans 8 would be a good chapter to read on this subject. In particular, vs. 38-39:
"For I am convinced that neither death, nor life, nor principalities, nor present things, nor future things, nor powers, nor height, nor depth, nor any other creature will be able to separate us from the love of God in Christ Jesus our Lord".