Jesus taught we should not fear those who can kill our bodies but not harm our souls. Rather, the only one we should fear is the One who can destroy both our body and soul in Hell (Matthew 10:28). Fear is inevitable for all of us, but we must fear the right things. If we fear the wrong things, we will live our lives without joy and even in a state of paralysis.
Those who know Christ need not fear anything in this world. Everything here is temporary, so anything we would fear will be temporary as well. Recognizing all pain, discomfort, sickness, or need is temporary should alleviate much of the anxiety we tend to feel.